Method for optimized design and fabrication of three dimensional trusses based on relaxed modularity constraints

Abstract

Method for optimized design and fabrication of three dimensional trusses based on relaxed modularity constraints SOLUTION: A method for layout optimization of initial design, recognition of module arrangement by data clustering, design of relaxed modularization constraint, geometrical optimization and manufacturing and integrated assembly steps by 3D printing, wherein an iterative method is used to automatically design a three-dimensional truss structure comprising a plurality of module types, and a data clustering method is introduced into the iterative process to recognize the module arrangement, and a relaxed modularization constraint is applied to gradually lead the optimization solution to a modularized structure, and a method for iteratively solving the recognition of the module arrangement by data clustering and the design of relaxed modularization constraint is proposed. To further clarify a load transmission path of a structure, and to remarkably improve calculation efficiency while minimizing influence on a final optimized structure volume.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This application belongs to the technical fields of structural engineering and additive manufacturing, and in particular to a method for optimizing the design and manufacturing of three-dimensional trusses based on relaxed modularity constraints. [Background technology]

[0002] Due to its advantages of low cost, high quality, and fast construction speed, modular construction has been widely applied in the field of civil engineering, and is used in the structural design and construction of prefabricated buildings, deployable bridges, etc. However, the design of modular construction is not only related to the local modular structure but also to the overall module arrangement. To fully realize the potential of modular construction, there is a strong demand for related design digitalization methods.

[0003] Continuum topology optimization represents one of the major trends in structural design and is based on elastic design theory and finite element discrete methods. Continuum topology optimization methods include penalized solid isotropic materials, bidirectional evolutionary structural optimization (BESO), level set methods, moving morphable components (MMC), and moving morphable voids (MMV).

[0004] The concept of modular structures has been widely applied in structural optimization, most of which are based on continuum topology optimization methods. There are two main branches: one focuses on the topology design of microstructures, regarding modular cells as infinitesimal relative to the design domain and adopting homogenization methods; the other focuses on the topology design of macrostructures, using pioneering techniques to design optimized structures formed from a small number of prescribed building modules.

[0005] However, research on topology optimization of truss continua often relies on predefined modules or only uses one module type. Simultaneously optimizing the structure and layout of modules and combining multiple module types can effectively reduce the increase in structural volume due to modularity constraints. However, given the complexity of the design problem, this method also incurs high computational costs, limiting its application to large-scale three-dimensional truss optimization problems. In the field of structural design, metaheuristic algorithms can be used to solve complex optimization problems, including genetic algorithms, heuristic particle swarm optimization, and ant colony optimization. Combining different evolutionary policies can fully utilize their respective advantages and incorporate initial feasible solutions into specific algorithms to improve computational efficiency. Therefore, how to use truss layout optimization methods to design multi-type modular structures remains a challenging research topic.

[0006] In light of the above, it is extremely necessary to research new methods for optimizing the design and manufacturing of three-dimensional trusses, significantly reducing costs while minimizing the change in structural volume, and realizing the optimization of modular unit layout, 3D printing manufacturing, and integrated assembly of large-scale and complex three-dimensional truss structures. Summary of the Invention [Problem to be solved by the invention]

[0007] The objective of this application is to overcome the drawbacks of the prior art and to provide a method for the optimized design and manufacturing of three-dimensional trusses based on relaxed modularity constraints. [Means for solving the problem]

[0008] The optimization design and manufacturing method for a three-dimensional truss based on such relaxed modular constraints is as follows: A step S1 of optimizing the layout of the initial design, in which the layout of the initial design is optimized with the design goal of minimizing the total volume of the rod members, and an initial solution of the layout optimization is obtained and used as a strict lower bound; Step S2 of modularized design layout optimization, repeating steps S2.1 and S2.2 to refine the initial layout optimization solution into an optimal modularized design layout optimization solution; In step S2.1 of recognizing module placement by data clustering, the structural layout is checked using data clustering, module placement is recognized, and a solution to an optimization problem with strict modularization constraints is obtained; a step S2.2 of designing relaxed modularity constraints, using the module placement to re-optimize the structure through the relaxed modularity constraints; A geometric optimization step S3 is a step of performing post-processing by geometric optimization on the layout optimization result to obtain a rational and effective optimized structure; The method includes a step S4 of manufacturing and integral assembly by 3D printing, in which multiple types of optimized modularized units are manufactured by 3D printing, and the modularized units are assembled together to manufacture an optimized structure.

[0009] Preferably, in step 1, an objective function for designing the rod member so that the total volume of the rod member is minimized is expressed as follows: JPEG2026012653000002.jpg1232... (1) and The force balance equation, the stress constraint of the rod member, and the non-negative constraint of the cross-sectional area of ​​the rod member are introduced as constraints in equation (1), and the equation of the constraints is as follows: JPEG2026012653000003.jpg1826... (2) and In the formula, V is the total volume of the rod, JPEG2026012653000004.jpg612 is the length vector of the rod member, JPEG2026012653000005.jpg63 is the area vector of the rod member, JPEG2026012653000006.jpg613 is a balanced matrix, JPEG2026012653000007.jpg63 is the internal force vector of the rod member, JPEG2026012653000008.jpg62 is the nodal load vector, and σ c and σ t are the allowable compressive stress and allowable tensile stress of the bar member, respectively, JPEG2026012653000009.jpg1235 and JPEG2026012653000010.jpg1236 is the node JPEG2026012653000011.jpg62 coordinate vector and JPEG2026012653000012.jpg62 is a coordinate vector, JPEG2026012653000013.jpg62 is the number of nodes.

[0010] Preferably, in step S1, a design domain and boundary conditions are first defined, then the design domain is discretized into a nodal grid, a base structure including all possible connections between the nodes is constructed, an optimized subset structure is recognized from the base structure, variables are designed based on the nodal coordinates, and geometric optimization is performed.

[0011] Preferably, in step S2.1, data clustering separates objects in the dataset into different groups based on similarity, where the similarity is quantified using Euclidean distance, the formula of which is: JPEG2026012653000014.jpg1254... (3) and In the formula: JPEG2026012653000015.jpg1249 is the clustering dataset, where JPEG2026012653000016.jpg64 JPEG2026012653000017.jpg is the 63rd data cluster, JPEG2026012653000018.jpg62 is the total number of data clusters, i.e., it is equal to the number of module types in the optimization problem, JPEG2026012653000019.jpg62 is a data point belonging to JPEG2026012653000020.jpg64, JPEG2026012653000021.jpg1223 is the center of mass of JPEG2026012653000022.jpg64, where JPEG2026012653000023.jpg67 is the number of corresponding data points, A data clustering algorithm is used to extract modular configurations from the existing structure based on the obtained groups, i.e., firstly, the design domain and boundary conditions are given, and the domain volume is used as the clustering data, i.e., in Eq. (3), JPEG2026012653000024.jpg69, and obtain the optimal module placement, where JPEG2026012653000025.jpg64 is the domain volume, and finally the linear programming problem is solved to obtain the corresponding re-optimized modular optimization structure, and the solution of the strict modular optimization problem, i.e., the solution of the nominal lower bound, is obtained.

[0012] Preferably, in step S2.1, a strict modular constrained optimization problem is solved, where the objective function is: JPEG2026012653000026.jpg1238... (4) and The constraint formula is: JPEG2026012653000027.jpg2367... (5) and In the formula: JPEG2026012653000028.jpg63 is a binary constant that represents the jth module type number in each module space, and reflects whether the corresponding module type is active or not. JPEG2026012653000029.jpg62 is the number of module types, JPEG2026012653000030.jpg62 is the number of units, JPEG2026012653000031.jpg69 is the selectable area of ​​the rod member unit in the j-th module.

[0013] Preferably, in step S2.2, a predetermined structure of different module types is set, and a unit-based modularization constraint is set to ensure that the internal structures of the module spaces of the same module type are all the same. The module space is divided into d×d sub-regions, and each sub-region has its corresponding structure. The volume of the sub-region is constrained, and the formula is: JPEG2026012653000032.jpg1280... (6) JPEG2026012653000033.jpg1245... (7) and In the formula: JPEG2026012653000034.jpg613 is the structural volume of the b-th subregion in the k-th module space, JPEG2026012653000035.jpg613 is the total volume of the bth module region in the jth module type, JPEG2026012653000036.jpg64 is the index set of the module space when the jth module type is adopted, JPEG2026012653000037.jpg68 is the b-th subregion in the k-th module space, JPEG2026012653000038.jpg69 and JPEG2026012653000039.jpg68 are the cross-sectional area and length of the rod member unit in the b-th sub-region, respectively, and m is the rod member number. If the value of d is sufficiently large, the region-based modularization constraint approaches the unit-based modularization constraint, and if the value of d is relatively small, the region-based modularization constraint becomes equivalent to the relaxed modularization constraint. In this case, the fourth equation in equation (5) can be replaced with equations (6) and (7) to obtain the relaxed modularization constraint design equation.

[0014] Preferably, in step S2.2, the modularization constraint can be strengthened by systematically increasing the value of d. To solve the convergence problem caused by the faulting of the sub-region due to the increase in the value of d, Equation (6) is modified to Equation (8), which is: JPEG2026012653000040.jpg12110... (8) and In the formula: r is the influence coefficient, 0≦r≦1. When r=1, it means that constraint (6) has been completely removed. When r=0, it means that constraint (6) has been fully applied, i.e., a stricter modularization constraint has been imposed. Throughout the iteration process, the value of r starts from a value close to 1 and gradually decreases to 0.

[0015] In step S2.2, we solve the strict modular constrained optimization problem, where the objective function is JPEG2026012653000041.jpg1241... (9) and The constraint formula is: JPEG2026012653000042.jpg29112... (10) and In the equation, the constraint equation (10) is composed of the first three equations of equation (5), equation (7) and equation (8).

[0016] Preferably, in step S2, an improved iteration strategy is adopted between step S2.1 and step S2.2 to improve the final optimization result, specifically, after step S2.1 is completed: For JPEG2026012653000043.jpg616, update the module placement and then perform step S2.2 to solve the optimization problem with the relaxed modularization constraint; For JPEG2026012653000044.jpg615, step S2.2 is directly implemented to solve the optimization problem with the relaxed modularity constraint, where: JPEG2026012653000045.jpg64 is the volume of the modular optimized structure, which is solved using equation (5), JPEG2026012653000046.jpg62 is the number of iterations, JPEG2026012653000047.jpg2355 is the maximum number of iterations configured. [Effects of the Invention]

[0017] The beneficial effects of the present invention are as follows:

[0018] 1) The present invention provides a method for optimizing the design and manufacturing of a three-dimensional truss structure based on relaxed modularity constraints. It uses an iterative method to automatically design a three-dimensional truss structure containing multiple module types. By introducing a data clustering method into the iterative process to identify the module layout and applying relaxed modularity constraints, the optimization solution gradually leads to a modular structure. As a result, the three-dimensional truss optimization result has the characteristics of a multi-type modular structure, which is relatively easy to manufacture.

[0019] 2) The method for optimizing the design and manufacturing of a three-dimensional truss based on relaxed modular constraints provided by this application not only optimizes the truss layout in the initial design, but also proposes an iterative solution method for recognizing the module arrangement through data clustering and using relaxed modular constraint design to address the problem of excessive computational complexity when solving large-scale three-dimensional truss optimization problems. This makes the load transfer path of the structure clearer, significantly improving computational efficiency while minimizing the impact on the final optimized structural volume.

[0020] 3) The method for optimizing the design and manufacturing of a three-dimensional truss based on relaxed modular constraints provided by this application uses an iterative solution method that recognizes module placement through data clustering based on a mathematical model of truss layout optimization, achieving rapid and efficient solution based on relaxed modular constraints. By setting relaxed modular constraints for multiple types of modules, modular reproducibility and structural regularity of the optimization results are achieved. 3D printing optimization design and integrated assembly manufacturing of complex three-dimensional truss optimized structures are realized through 3D modeling, modular structural model slicing, print path generation, and integrated assembly manufacturing. [Brief explanation of the drawings]

[0021] [Figure 1] FIG. 1 is a schematic diagram of the overall optimization flow of steps 2 and 3 of the present application. [Figure 2] 2A is a schematic diagram of the process of step S1 of optimizing the layout of the initial design (FIG. 2A is a schematic diagram of defining the design domain and boundary conditions, FIG. 2B is a schematic diagram of the generated basic structure, FIG. 2C is a schematic diagram of recognizing the optimized subset structure, and FIG. 2D is a schematic diagram of the geometric optimization). [Figure 3] 3A is a schematic diagram of the process of step S2.1 of recognizing module placement by data clustering (FIG. 3A is a schematic diagram of a given design domain and boundary conditions, FIG. 3B is a schematic diagram of recognizing module placement by data clustering, and FIG. 3C is a schematic diagram of a strict modular constraint re-optimization structure). [Figure 4]4A is a schematic diagram of the structure of arranging different module types; FIG. 4B is a schematic diagram of setting unit-based modularization constraints; FIG. 4C is a schematic diagram of relaxed modularization constraints; and FIG. 4D is a schematic diagram of region-based relaxed modularization constraints. [Figure 5] FIG. 1 is a schematic diagram of a semi-structural model of an example of a simply supported bridge. [Figure 6] FIG. 1 is a schematic diagram of an iterative process for a simply supported bridge embodiment. [Figure 7] FIG. 10 is a diagram showing how the structure volume, the variable d, and the variable r change during the iterative process. [Figure 8] 8A is a schematic diagram of a module arrangement of a square roof structure (FIG. 8A is a plan view of the square roof structure, and FIG. 8B is a front view of the square roof structure). [Figure 9] 3D schematic diagram of full-span vertical loads on a square roof structure. [Figure 10] 10A and 10B show the optimization results of a square roof structure for six different module types (FIG. 10A is a plan view of the optimization results, FIG. 10B is an axonometric projection view of the optimization results, and FIG. 10C is a schematic view of the six different module types). DETAILED DESCRIPTION OF THE INVENTION

[0022] The present application will be further described below in connection with examples. The following description of the examples is only to facilitate understanding of the present application. It should be noted that those skilled in the art can make some modifications to the present application without departing from the principles of the present application, and these improvements and modifications are also included in the scope of protection of the claims of the present application. [Example]

[0023] Example 1 As an example, a method for optimizing the design and manufacturing of a three-dimensional truss based on such relaxed modular constraints may include: In step S1, the layout of the initial design is optimized. As shown in Figures 2A to 2D, step S1 mainly includes the following steps: in step S1.1, as shown in Figure 2A, a design domain and boundary conditions are defined; in step S1.2, as shown in Figure 2B, the design domain is discretized into a nodal grid and a base structure including all possible connections between the nodes is constructed; in step S1.3, as shown in Figure 2C, an optimized subset structure is recognized from the base structure; and in step S1.4, as shown in Figure 2D, a reasonable optimization result is obtained using geometric optimization based on the design variables of the nodal coordinates.

[0024] In step S1, the layout of the initial design is optimized using equations (1) and (2) without considering the modularization requirements, and an initial solution for the layout optimization is obtained as a strict lower bound. The objective function, whose design goal is to minimize the total volume of the rod members, is JPEG2026012653000048.jpg1232... (1) and The constraint formula is: JPEG2026012653000049.jpg1826... (2) and In the formula, V is the total volume of the rod, JPEG2026012653000050.jpg612 is the length vector of the rod member, JPEG2026012653000051.jpg63 is the area vector of the rod member, JPEG2026012653000052.jpg613 is a balanced matrix, JPEG2026012653000053.jpg63 is the internal force vector of the rod member, JPEG2026012653000054.jpg62 is the nodal load vector, and σ c and σ t are the allowable compressive stress and allowable tensile stress of the bar member, respectively, JPEG2026012653000055.jpg1235 and JPEG2026012653000056.jpg1236 is the node JPEG2026012653000057.jpg62 coordinate vector and JPEG2026012653000058.jpg62 is a coordinate vector, JPEG2026012653000059.jpg62 is the number of nodes.

[0025] The three constraints in equation (2) represent the force balance equation, the stress constraint of the bar member, and the non-negative constraint of the cross-sectional area of ​​the bar member, respectively. The design variables are the area vector of the bar member, JPEG2026012653000060.jpg63, Internal force vector of rod member JPEG2026012653000061.jpg63 and coordinates JPEG2026012653000062.jpg68, JPEG2026012653000063.jpg613 and JPEG2026012653000064.jpg612 are the matrix and vector generated based on the topology method of the rod member, respectively. JPEG2026012653000065.jpg62 is a constant vector corresponding to the actual operating situation, JPEG2026012653000066.jpg64 and JPEG2026012653000067.jpg64 are all constants that correspond to actual operating conditions.

[0026] In step S2, the layout of the modularized design is optimized, specifically, the initial solution of layout optimization obtained in step S1 is refined into an optimal solution of the modularized design for layout optimization by considering the modularization requirements and going through iterations, each iteration consisting of two main steps.

[0027] In step S2.1, the module arrangement is recognized by data clustering, and the module arrangement is solved by the data clustering grouping formula (3), and the structural layout is checked using data clustering to recognize the relevant module arrangement. Data clustering is an unsupervised learning algorithm that can divide objects in a dataset into different groups based on similarity, which is quantified using Euclidean distance, and the formula is: JPEG2026012653000068.jpg1254 (3) and In the formula: JPEG2026012653000069.jpg1249 is the clustering dataset, where JPEG2026012653000070.jpg64 JPEG2026012653000071.jpg is the 63rd data cluster, JPEG2026012653000072.jpg62 is the total number of data clusters, i.e., it is equal to the number of module types in the optimization problem. JPEG2026012653000073.jpg62 is a data point belonging to JPEG2026012653000074.jpg64, JPEG2026012653000075.jpg1223 is the center of mass of JPEG2026012653000076.jpg64, where JPEG2026012653000077.jpg, where 67 is the number of corresponding data points, A data clustering algorithm is used to extract modular configurations from the existing structure based on the obtained groups, i.e., firstly, the design domain and boundary conditions are given, and the domain volume is used as the clustering data, i.e., in Eq. (3), JPEG2026012653000078.jpg69, and obtain the optimal module placement, where JPEG2026012653000079.jpg64 is the domain volume, and finally the linear programming problem is solved to obtain the corresponding re-optimized modular optimization structure, and the solution of the strict modular optimization problem, i.e., the solution of the nominal lower bound, is obtained. In step S2.2, relaxed modularization constraints are designed, specifically, the initial solution is modified into a more modular design by utilizing the identified module placement and re-optimizing the structure by applying the relaxed modularization constraints.

[0028] In step S3, the structure is manufactured and assembled into an integrated unit by 3D printing. Specifically, 3D modeling is performed, and multiple types of modularized units in the optimized model are sliced ​​to generate print paths, which are then manufactured by 3D printing, and the modularized units are assembled into an integrated unit to produce the optimized structure. [Example]

[0029] Example 2 As another embodiment, this embodiment 2 proposes a more specific optimization design and manufacturing method for a three-dimensional truss based on relaxed modular constraints based on the first embodiment, and in step S2: As shown in Figures 3A to 3C, in step S2.1, a data clustering algorithm is used to extract a modularized layout from an existing structure, and the main steps are as follows: in step S2.1.1, as shown in Figure 3A, a design domain and boundary conditions are given; in step S2.1.2, as shown in Figure 3B, the domain volume is used as the clustering data, i.e., ζ = v in Eq. (3). s and obtain the optimal module placement, where v s is the domain volume, and in S2.1.3, as shown in Figure 3C, the linear programming problem is solved to obtain the corresponding re-optimized modular optimization structure, and the solution to the optimization problem with strict modular constraints, i.e., the nominal lower bound solution, is shown in equations (4) and (5). In this embodiment, a cantilever beam is taken as an example, The objective function is JPEG2026012653000080.jpg1238... (4) and The constraint formula is: JPEG2026012653000081.jpg2367... (5) and In the formula: JPEG2026012653000082.jpg63 is a binary constant that represents the jth module type number in each module space, and reflects whether the corresponding module type is active or not. JPEG2026012653000083.jpg62 is the number of module types, JPEG2026012653000084.jpg62 is the number of units, JPEG2026012653000085.jpg69 is the selectable area of ​​the rod member unit in the j-th module.

[0030] Since data clustering algorithms can lead to suboptimal solutions, to determine the optimal module placement and the nominal lower bound solution, Set as JPEG2026012653000086.jpg69.

[0031] In step S2.2, as shown in Figures 4A to 4D, the main steps of relaxing the modularization constraint include the following: In step S2.2.1, a predetermined structure of different module types is set, as shown in Figure 4A. In step S2.2.2, a unit-based modularization constraint is set to ensure that the internal structures of module spaces belonging to the same module type are all the same. The structures of I, II, and III in Figure 4A are the same, and a specific schematic diagram of the module structure is shown in Figure 4B. In step S2.2.3, as shown in Figure 4C, the module space is divided into d x d subregions and the volumes of the subregions are constrained. In step S2.2.4, when the value of d is sufficiently large, the region-based modularization constraint approaches the result of the unit-based modularization constraint. Therefore, by setting the value of d relatively small, the region-based modularization constraint becomes equivalent to the relaxed modularization constraint (Figure 4D). The relaxed modularization constraint is expressed as equations (6) and (7), which replace the fourth equation in equation (5). JPEG2026012653000087.jpg1280... (6) JPEG2026012653000088.jpg1245... (7)

[0032] In the formula: JPEG2026012653000089.jpg613 is the structural volume of the b-th subregion in the k-th module space, JPEG2026012653000090.jpg613 is the total volume of the bth module region in the jth module type, JPEG2026012653000091.jpg64 is the index set of the module space when the jth module type is adopted, JPEG2026012653000092.jpg68 is the b-th subregion in the k-th module space, JPEG2026012653000093.jpg69 and JPEG2026012653000094.jpg68 are the cross-sectional area and length of the rod member unit in the b-th sub-region, respectively, and m is the rod member number. During the optimization process, systematically increasing the value of d can effectively strengthen the modularity constraint. However, increasing the value of d can also cause subdomain faults, and such sudden faults can cause significant changes between iterations, leading to convergence problems. To solve this convergence problem and ensure a smooth transition between iterations, we modify constraint (6) with the more gradual constraint (8). JPEG2026012653000095.jpg12110... (8) In the formula, r is the influence coefficient, 0≦r≦1. When r=1, it means that constraint (6) has been completely removed. When r=0, it means that constraint (6) has been fully applied, i.e., a stricter modularization constraint is implemented. Throughout the iteration process, the value of r starts from a value close to 1 and gradually decreases to 0, thereby gradually implementing a stricter modularization constraint.

[0033] In step S2.2, the formulation of the relaxed modular constrained optimization problem is solved, where the objective function is JPEG2026012653000096.jpg1241... (9) and The constraint formula is: JPEG2026012653000097.jpg29112... (10) and In the equation, the constraint equation (10) is composed of the first three equations of equation (5), equation (7) and equation (8).

[0034] Furthermore, between step S2.1 and step S2.2, an improved iteration strategy is adopted to improve the final optimization result. Specifically, after step S2.1 is completed, For JPEG2026012653000098.jpg616, update the module placement and then perform step S2.2 to solve the optimization problem with the relaxed modularization constraint; For JPEG2026012653000099.jpg615, step S2.2 is directly implemented to solve the optimization problem with the relaxed modularity constraint, where: JPEG2026012653000100.jpg64 is the volume of the modular optimized structure, which is solved using equation (5), JPEG2026012653000101.jpg62 is the number of iterations, JPEG2026012653000102.jpg2355 is the maximum number of iterations configured.

[0035] Step S3 specifically performs post-processing of the layout optimization result by geometric optimization to obtain a reasonable and effective optimized structure.

[0036] Specifically, step S4 extracts structural information of the modularized units based on the optimization results. The structural information includes the modularized unit mode, modularized unit position, modularized unit connection, and cross-sectional dimensions of the modularized unit rods. After the modularized unit rod assembly and node generation processes, a 3D real model is created, and various modularized units in the real model are sliced, print paths are generated, and the modularized units are manufactured by 3D printing. Next, the modularized units are connected and assembled together to manufacture the optimized structure.

[0037] Note that, since the same or similar parts of this embodiment as those of the first embodiment can be mutually referenced, the description thereof will be omitted in this application. [Example]

[0038] Example 3 As another example, Example 3 is proposed based on Example 1 and Example 2, and performs optimization design and manufacturing of a simply supported bridge based on the solution results of step S1 of optimizing the layout of the initial design and step S2 of optimizing the layout of the modularized design in the method for optimizing design and manufacturing of a three-dimensional truss based on such relaxed modularization constraints.

[0039] As shown in Figure 5, the optimization design was performed based on symmetry by taking the semi-structure of this simply supported bridge. Specifically, a 5m x 2m design area was taken, and a vertical load F = 0.5N was applied to the lower right of the design area. The module size was 0.5m x 0.5m, the number of module types p = 4, and the module complexity was 4 x 4. The optimization results at each step were expanded to the full size based on symmetry. Figure 6 shows the changes in the structure during the optimization process. Figure 7 shows the changes in the structural volume, variable d, and variable r during the iterative process.

[0040] First, the layout of the initial design is optimized in step S1 according to equations (1) and (2), and the optimization result is obtained as shown in the upper left of FIG.

[0041] Next, in step S2.1 of recognizing module placement by data clustering, the unit area data of the layout optimization of the initial design in Figure 6 is used to perform grouping by data clustering according to Equation (3), laying the foundation for developing the initial modularization structure.

[0042] Next, by solving the optimization equations (4) to (5) with strict modularization constraints, we obtain the module placement optimization result as shown in the upper right corner of Figure 6 .

[0043] In each iteration, we apply the optimization formulas (9) to (10) in step S2.2 to design relaxed modularization constraints, and obtain intermediate optimization results such as the results on the left side of lines 2 to 4 in Figure 6. As the optimization progresses, the degree of relaxation decreases, and the intermediate optimization results are guided to a modularization structure.

[0044] By updating the module placement accordingly, as shown in the right side of lines 2 to 4 in Figure 6, the volume of the corresponding modularized structure is reduced, as shown in Figure 7. In this example, the iterative process ends at the 11th iteration, when d = 3, r = 0.4, and the optimized volume is 25.04 × 10 -6 m 3 is.

[0045] Finally, the structure was streamlined through geometric optimization, and the results in the bottom left of Figure 6 were obtained. By simplifying the internal structure of each type of module and removing modules without stress, the structural volume was reduced to 23.00 × 10 -6 m 3 was further reduced to

[0046] The optimization results of the two-stage optimization method are shown in the lower right of Figure 6. The structural volume corresponding to the optimization results of the present method was reduced by approximately 2.2%, and the CPU calculation time required was only 53 seconds, while the two-stage optimization method required 10,951 seconds. Therefore, the CPU calculation time of the present method was reduced by 99.50%, and the calculation efficiency was significantly improved.

[0047] Figure 7 shows the change in modularized structural volume throughout the iteration process. Except for the fourth iteration, the structural volumes generated by most iterations are the same as or improved from the results of the previous steps. After six iterations, the changes in module arrangement and structural volume are small, confirming that the algorithm has converged. [Example]

[0048] Example 4 As another example, Example 4, based on Examples 1 and 2, proposes the application of the optimization design and manufacturing method for a three-dimensional truss based on such relaxed modular constraints to a three-dimensional truss model of a square roof under four-side support conditions.

[0049] As shown in Figures 8A and 8B, a 60m-span square roof truss structure was optimized. Based on symmetry, a simplified analysis was performed considering a quarter-span structure. The full-size roof structure includes a 12x12x2 modular grid, employing six different module types, each with a complexity of 3x3x3. Supports are installed at 10m intervals along the four edges of the structure. To accurately simulate the effect of gravity load G, a vertical load, i.e., a full-span load, was applied to each node on the top surface of the structure, as shown in Figure 9.

[0050] As shown in Figures 10A to 10C, the optimized volume of the six different module types in Figure 10C is 5462 x 10 in the operating condition of full span load after optimization by the method of the present invention. -6 m 3 The optimization solution time was 1289 seconds. As a comparison example, when a solution was run using one module type, the corresponding optimized volume was 8614 × 10 -6 m 3 The results showed that increasing the number of module types from 1 to 6 could reduce the volume by up to 36.5%.

[0051] As can be seen from Examples 3 and 4, the present invention provides a method for optimizing the design and manufacturing of a three-dimensional truss structure based on relaxed modular constraints. Based on a mathematical model of truss layout optimization, the method uses an iterative solution method that recognizes module placement through data clustering, achieving rapid and efficient solutioning based on relaxed modular constraints. By setting relaxed modular constraints for multiple types of modules, the optimization results achieve modular reproducibility and structural regularity. The impact on the volume of the final optimized structure is minimized, while significantly improving computational efficiency. By combining 3D modeling, modular structural model slicing, print path generation, and integrated assembly manufacturing, the present invention achieves 3D printing optimization design and integrated assembly manufacturing of a complex three-dimensional truss optimized structure. Furthermore, practical verification has demonstrated that the present method is effective.

[0052] Each embodiment in this specification will be described in an incremental manner, with emphasis on the differences between each embodiment and other embodiments, and reference will be made to each other for similar or similar parts between the embodiments.

Claims

1. A method for optimization design and manufacturing of three-dimensional trusses based on relaxed modularity constraints, comprising: a step S1 of optimizing the layout of the initial design, in which the layout of the initial design is optimized with the design goal of minimizing the total volume of the rod members, and an initial solution of the layout optimization is obtained and used as a strict lower limit; A modularized design layout optimization step S2, repeating steps S2.1 and S2.2 to refine the initial layout optimization solution into an optimal modularized design layout optimization solution; In a step S2.1 of recognizing module placement by data clustering, data clustering is used to check the structural layout, recognize module placement, and solve an optimization problem with strict modularization constraints; a step S2.2 of designing relaxed modularity constraints, using the module placement to re-optimize the structure through the relaxed modularity constraints; A geometric optimization step S3, in which the layout optimization result is subjected to post-processing by geometric optimization to obtain a reasonable and effective optimization result; a step S4 of manufacturing and integral assembly by 3D printing, in which a plurality of types of optimized modularized units are manufactured by 3D printing, and the modularized units are integrally assembled to manufacture an optimized structure; A method for optimizing the design and manufacturing of three-dimensional trusses based on relaxed modular constraints, comprising:

2. In step 1, the objective function for designing the rod member to minimize its total volume is: ・・・・ （１） and The force balance equation, the stress constraint of the rod member, and the non-negative constraint of the cross-sectional area of ​​the rod member are introduced as constraint conditions in equation (1), and the equation of the constraint conditions is as follows: ・・・・ （２） and where V is the total volume of the rod, is the length vector of the rod, is the area vector of the rod, is the balanced matrix, is the internal force vector of the rod member, is the nodal load vector, and σ c and σ t are the allowable compressive stress and allowable tensile stress of the bar member, respectively, and are the nodes Coordinate vector and is a coordinate vector, is the number of nodes The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 1.

3. In step S1, first, a design domain and boundary conditions are defined, then the design domain is discretized into a nodal grid, a basic structure including all possible connections between the nodes is constructed, an optimized subset structure is recognized from the basic structure, variables are designed based on the nodal coordinates, and geometric optimization is performed. The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 1.

4. In step S2.1, data clustering separates objects in the dataset into different groups based on similarity, which is quantified using Euclidean distance, the formula of which is: ・・・・ （３） and In the formula: is the clustering dataset, where teeth is the th data cluster, is the total number of data clusters, i.e., equal to the number of types of modules in the optimization problem, teeth are data points that belong to teeth is the center of mass of is the number of corresponding data points, A data clustering algorithm is used to extract modular configurations from the existing structure based on the obtained groups, i.e., firstly, the design domain and boundary conditions are given, and the domain volume is used as the clustering data, i.e., in Equation (3), and obtain the optimal module placement, where is the domain volume, and finally solve the linear programming problem to obtain the corresponding re-optimized modular optimization structure, and then solve the exact modular optimization problem, i.e., the nominal lower bound solution. ・・・・ （３） and In the formula: is the clustering dataset, where teeth is the th data cluster, is the total number of data clusters, i.e., equal to the number of types of modules in the optimization problem, teeth are data points that belong to teeth is the center of mass of is the number of corresponding data points, Using a data clustering algorithm, a modular configuration is extracted from the existing structure based on the obtained group. That is, first, the design domain and boundary conditions are given, and the domain volume is used as the clustering data. That is, ζ = v_s in Equation (3) is used to obtain the optimal modular configuration, where v_s is the domain volume. Finally, a linear programming problem is solved to obtain the corresponding re-optimized modular optimization structure. The solution to the strict modular optimization problem, i.e., the solution to the nominal lower bound, is obtained. The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 1.

5. In step S2.1, a strict modular constrained optimization problem is solved, where the objective function is ・・・・ （４） and The constraint formula is: ・・・・ （５） and In the formula: is a binary constant representing the jth module type number in each module space, reflecting whether the corresponding module type is active or not, is the number of types of modules, is the number of units, is the selectable area of ​​the rod unit in the j-th module The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 4.

6. In step S2.2, a predetermined structure of different module types is set, and the unit-based modularization constraint is set as a relaxed modularization constraint to ensure that the internal structures of the module spaces of the same module type are all the same. The module space is divided into d×d subregions, and each subregion has its corresponding structure. The volume of the subregion is constrained by the formula: ・・・・ （６） ・・・・ （７） and In the formula: is the structural volume of the b-th subregion in the k-th modular space, is the total volume of the bth module region in the jth module type, is the index set of the module space when the j-th module type is adopted, is the b-th subregion in the k-th module space, and are the cross-sectional area and length of the rod unit in the b-th sub-region, respectively, m is the rod number, When the value of d is sufficiently large, the region-based modularity constraint approaches the unit-based modularity constraint. When the value of d is relatively small, the region-based modularity constraint becomes equivalent to the relaxed modularity constraint. In this case, the fourth equation in equation (5) can be replaced with equations (6) and (7) to obtain the relaxed modularity constraint design equation. The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 5.

7. In step S2.2, the modularity constraint can be strengthened by systematically increasing the value of d. To solve the convergence problem caused by the faulting of the sub-region due to the increase in the value of d, Equation (6) is modified to Equation (8), which is: ・・・・ （８） and In the formula, r is an influence coefficient, and 0≦r≦1. When r=1, it means that the constraint (6) has been completely removed. When r=0, it means that the constraint (6) has been fully applied. Throughout the iteration process, the value of r starts from a value close to 1 and gradually decreases to 0. The method for optimizing design and manufacturing of three-dimensional trusses based on relaxed modular constraints according to claim 6.

8. In step S2.2, the formulation of the relaxed modular constrained optimization problem is solved, where the objective function is ・・・・ （９） and The constraint formula is: ・・・・ （１０） and In the equation, the constraint equation (10) is composed of the first three equations of equation (5), equation (7) and equation (8). The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 1.

9. In step S2, between step S2.1 and step S2.2, an improved iteration strategy is adopted to improve the final optimization result, specifically, after step S2.1 is completed: If , update the module placement and then perform step S2.2 to solve the optimization problem with relaxed modularization constraints; If , then step S2.2 is performed directly to solve the optimization problem with relaxed modularity constraints, where is the volume of the modular optimized structure, solved using equation (5), is the number of iterations, is the maximum number of iterations set The method for optimizing design and manufacturing of a three-dimensional truss based on relaxed modular constraints according to claim 5.

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