Optimized design and manufacturing process for a three-dimensional truss based on a relaxed modular constraint

Abstract

The present invention relates to a method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint, which includes the following steps: layout optimization of an initial design, identification of the module layout by data grouping, design of relaxed modular constraints, geometric optimization, manufacturing by 3D printing and full assembly.The beneficial effects of the present invention are as follows: an iterative process is used to automatically design a three-dimensional truss structure comprising several types of modules; a data grouping process is introduced during the iterative process to identify the arrangement of the modules; the optimization solution gradually tends towards a modular structure by imposing a relaxed modular constraint; thus, the optimized 3D truss exhibits characteristics of several types of modular structures and is relatively easy to manufacture. Figure to be published with the abstract: Figure 1.

Description

Title of the invention: Optimized design and manufacturing method for a three-dimensional truss based on a relaxed modular constraint technical field

[0001] The present invention relates to the field of structural engineering and additive manufacturing technology, and more particularly to a method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint.

[0002]

[0003] TECHNIQUE CONTEXT

[0004] Modular structures are widely used in civil engineering for the structural design and construction of assembled buildings, deployable bridges, and other structures, thanks to their low cost, high quality, and rapid construction. However, the design of modular structures involves not only the local modular structure but also the overall modular arrangement; relevant digital design processes are urgently needed to unlock the full potential of modular structures.

[0005] Optimization of continuum topology represents a major trend in structural design, based on elastic design theory and finite element discretization; continuum topology optimization methods include the isotropic solid materials method with penalty, the bidirectional asymptotic structural optimization (BESO) method, the set of levels method, the removable deformed components method, and the removable deformed holes method.

[0006] The concept of modular structures is widely used in structural optimization, most of which are based on continuum topology optimization processes. It mainly consists of two branches, one focused on the topological design of microstructures, in which modular cellular elements are considered infinitely small compared to the design domain and homogenization processes are used, and the other focusing on the topological design of macrostructures, in which optimized structures are formed from a small number of prescribed building blocks using pioneering techniques.

[0007] However, research on the topological optimization of farm continua often relies on predefined modules or uses only one type of module. Combining multiple module types through simultaneous optimization of both the structure and module layout can effectively reduce the increase in structural volume caused by modularity constraints. However, given the complexity of the design problem, this approach also results in a high computational cost, limiting its application to large-scale 3D truss optimization problems. In the field of structural design, complex optimization problems can be solved using metaheuristic algorithms, including genetic algorithms, particle swarm optimization heuristics, and ant colony optimization algorithms, among others.Combining different evolutionary strategies allows for the full exploitation of their respective advantages, and initially feasible solutions can be integrated into specific algorithms to improve computational efficiency. Therefore, the current research challenge is to determine how to design multi-type modular structures using truss layout optimization processes.

[0008] In summary, it is essential to study a new optimized design and manufacturing process for a three-dimensional truss in order to significantly reduce costs while structural volume changes are very small, and to achieve the optimization of modular unit layout, 3D printing manufacturing and integrated assembly of complex 3D truss structures on a large scale.

[0009] DISCLOSURE OF THE INVENTION

[0010] In order to resolve the drawbacks of the prior art, the present invention aims to propose an optimized design and manufacturing method for a three-dimensional truss based on a relaxed modular constraint.

[0011] The optimized design and manufacturing process for a three-dimensional truss based on a relaxed modular constraint comprises the following steps:

[0012] SI: layout optimization of an initial design: perform a layout optimization of an initial design by taking a minimum total volume of all the truss rods as the design objective in order to obtain an initial solution of a layout optimization, and take the initial solution as a strict lower bound;

[0013] S2: layout optimization of a modular design: repeat step S2.1 and step S2.2, and refine the initial layout optimization solution into a modular design layout optimization solution;

[0014] S2.1: Identification of module layout by data grouping: adopt the grouping of data to verify the structural layout and identify the layout of modules, in order to solve the problem of optimizing strict modular constraints;

[0015] S2.2: Design of relaxed modular constraints: use the arrangement of modules to re-optimize the structure thanks to the relaxed modular constraints;

[0016] S3: geometric optimization: perform a geometric optimization post-processing on a layout optimization result in order to obtain a reasonable and efficient optimization result;

[0017] S4: 3D printing manufacturing and full assembly: to carry out the 3D printing manufacturing of a plurality of optimized modular units, and to fully assemble the modular units in order to manufacture an optimized structure.

[0018] Preferably, in step SI, an objective function corresponding to the design objective of minimizing the total volume of all the stems in the truss is as follows:

[0019] [Math.l] minV = 7(x,y) T a# ( 1)

[0020] a force equilibrium equation, a rod force stress and a non-negative rod surface stress are introduced as stress conditions of formula (1), in which the expression of the stress conditions is as follows:

[0021] [Math.2] ' B(x,y)q = f • -aca <q<ata # (2) . a> 0

[0022] where: V is the total volume of all the rods in the truss, 1(X, y) is a rod length vector, a is a rod area vector, and is a matrix of equilibrium, 9 is an internal force vector of the rod, f is a load vector of a node, and are allowable compressive and tensile resistances of the rod, respectively; x = [ Xp X2, ..., X;] T and y = [ yfy? ..., y JT are an x ​​coordinate vector of the node and a y coordinate vector of the node, respectively, and 1 is the number of nodes.

[0023] Preferably, in the SI step, first, the definition of a design domain and boundary conditions, then, the discretization of the design domain into a grid of nodes and the construction of a basic structure containing all possible connections between the nodes; the identification of an optimized subset structure starting from the basic structure; and the realization of a geometric optimization based on node coordinate design variables.

[0024] Preferably, in step S2.1, the data grouping divides objects from a data set into different groups based on similarity, the similarity being quantified by a Euclidean distance, the expression being as follows:

[0025] [Math.3] argnûn^ScesJK-^ir* < 3 )

[0026] where: S = { Sp S2, ..., ..., Sp} is a set of grouped data, S¢ is the 0th data grouping, P is the total number of data groups, i.e., the number of module types in the optimization problem; Ç is a data point belonging to ; p — is a center of mass of and | is the number of corresponding data points;

[0027] extract a modular layout from the existing structure as a function of the grouping obtained and using a data grouping algorithm: first, define a design domain and boundary conditions, and take a volume of a region for data to be grouped, namely C = vs in formula (3), in order to obtain the optimal modular layout, vs being a volume of the region; and finally, solve the linear programming problem in order to obtain a corresponding modular optimization structure after reoptimization, and solve the strict modular optimization problem, namely a nominal lower bound solution.

[0028] Preferably, in step S2.1, the expression of the strict modular constraint optimization problem is solved, and the objective function is as follows:

[0029] [Math.4] minV = l(x, y) T a# (4) a,qAm^,y

[0030] The expression of the constraints is as follows:

[0031] [Math.5] 1 B(x,y)q = f -Πc a < qr < a t has ' a>0 #(5) = Life {1,2,

[0032] where: tj is a binary constant representing the number of the Jeme module type in each modular space, which reflects whether the corresponding module type is in an activated state; P is the number of module types, n is the number of units; Am j is an optional region of the stem unit in the Je me module.

[0033] Preferably, in step S2.2, the definition of given structures of different types of modules; the definition of modular constraints based on units, and ensuring that internal structures of module spaces of the same module type are the same; the division of the module space into dxd subregions, each subregion having a corresponding structure, and limiting a volume of the subregion, the expressions being as follows:

[0034] [Math.6] vS[k,b)= VkEHj,b= 1,2, d2# (6)

[0035] [Math.7] vsfk,b)= S mpQkbak^kjn # ( 7 )

[0036] where: vs / k,b) is a structural volume of the Same subregion in the Same modular space, is a total volume of the Same modular region of the Jth module type; Hj is a set of indices of the modular space when the Jth module type is adopted; is the Same subregion in the Same modular space; ak,m and lk are a cross-section and a length of the rod unit in the Same subregion, respectively, and m is the rod number;

[0037] for a sufficiently large value of d, modular constraints based on regions also converge to modular constraints based on units; for a relatively small value of d, modular constraints based on regions are also equivalent to relaxed modular constraints, according to which the fourth formula of expression (5) is replaced by expression (6) and expression (7), in order to obtain the design expression of relaxed modular constraints.

[0038] Preferably, in step S2.2, the modular constraints can be strengthened by systematically increasing the value of d; to resolve the convergence problem caused by a discrete jump in the subregion due to the increase in the value of d, expression (6) is modified into expression (8) as follows:

[0039] [Math.8] ( 1 -r) Vtijj»s VsiU)keHj, b =1,2, (8) where: r is an influencing factor, 0 < r < 1, when r = 1 it means that constraint expression (6) is completely eliminated, and when r = 0 it means that constraint expression (6) is completely applied, namely the stricter modular constraints; throughout the iteration the value of r gradually decreases from about 1 to 0.

[0040] Preferably, in step S2.2, the expression for the optimization problem of relaxed modular constraints is solved, and the objective function is as follows:

[0041] [Math.9] minV = l(x, y}Ta# (9)

[0042] The expression of the constraints is as follows:

[0043] [Math. 10] 1 B(x,y)q = f - aca < q < ata 1 a -° ,#(10) (1-r) vtUrb)< vs(k>b}< vtUrb> V keHjfb = 1,2, d ! vskk,b)= ^1I}Enk bakjn^km

[0044] in which the expression of the constraints (10) is composed of the first 3 formulas of expression (5), expression (7) and expression (8).

[0045] Preferably, in step S2, the adoption of an improved iterative implementation strategy between step S2.1 and step S2.2, in order to improve the final result of the optimization, specifically: at the end of step S2.1, when vç — VÇ-1, the update of the module layout, then the implementation of step S2.2 in order to solve the optimization problem of the relaxed modular constraints; when the direct implementation of step S2.2 in order to solve the optimization problem of the relaxed modular constraints; where: is a volume of the optimized modular structure, and which is solved using expression (5); £ is the number of iterations, and f max is the maximum number of iterations defined.

[0046] The beneficial effects of the present invention are as follows:

[0047] 1) in the process of optimized design and manufacture of a farm three-dimensional based on a relaxed modular constraint according to the present invention, an iterative process is used to automatically design a three-dimensional truss structure comprising several types of modules; a data grouping process is introduced during the iterative process in order to identify the arrangement of the modules; the optimization solution gradually tends towards a modular structure by imposing a relaxed modular constraint; thus, the optimized 3D truss exhibits characteristics of several types of modular structures and is relatively easy to manufacture.

[0048] 2) in the process of optimized design and manufacture of a farm three-dimensional based on a relaxed modular constraint according to the present invention, based on the optimization of the initially designed truss layout and in response to the problem that the computational volume is too large when solving large-scale three-dimensional truss optimization problems, the iterative solution comprising the identification of the module layout by Data grouping and the design of relaxed modular constraints is proposed so that the stress path of the structure is clearer and the efficiency of the calculation is remarkably improved subject to a low influence on the final optimized structure.

[0049] 3) in the optimized design and manufacturing process of a farm three-dimensional on the basis of a relaxed modular constraint according to the present invention, on the basis of the mathematical model of truss layout optimization, a fast and efficient solution based on relaxed modular constraints is achieved through the iterative solution comprising the grouping of data to identify the layout of modules; the modular repeatability and structural regularity of the optimization results are achieved by defining relaxed modular constraints of several types of modules; and the design of the optimization by 3D printing and the fabrication of integrated assemblies of the optimized three-dimensional truss structure are achieved through 3D modeling, modular cutting of the modular structure, printing path generation and integrated assembly production.

[0050] DESCRIPTION OF THE FIGURES

[0051] The [Fig.1] is a diagram of the overall optimization process at stages S2 and S3 according to the present invention;

[0052] FIG. 2 is a diagram of the layout optimization process for the initial design at the SI stage ([Fig.2a] is a diagram of the definition of the design domain and boundary conditions, [Fig.2b] is a diagram of the construction of a basic structure, [Fig.2c] is a diagram of the identification of an optimized subset structure, and [Fig.2d] is a diagram of a geometric optimization);

[0053] FIG. 3 is a diagram of the process of identifying the module layout by grouping data in step S2.1 ([Fig.3a] is a diagram of the definition of the design domain and boundary conditions, [Fig.3b] is a diagram of the identification of the module layout by grouping data, and [Fig.3c] is a diagram of the structural re-optimization using strict modular constraints);

[0054] FIG. 4 is a diagram of the process of designing relaxed modular constraints in step S2.2 ([Fig.4a] is a diagram of the arrangement of the different types of modules, [Fig.4b] is a diagram of the arrangement of modular constraints based on units, [Fig.4c] is a diagram of relaxed modular constraints, and [Fig.4d] is a diagram of relaxed modular constraints based on regions);

[0055] The [Fig.5] is a diagram of a semi-structural model of an embodiment of a simple supported beam bridge;

[0056] The [Fig.6] is a diagram of the iterative process of an embodiment of a simple supported beam bridge;

[0057] The [Fig.7] is a diagram of the variations in the volume of the structure, the variable d, and the variable r during the iterative process;

[0058] FIG. 8 is a module diagram of the square roof structure ([Fig.8a] is the top view of the square roof structure, [Fig.8b] is the front view of the square roof structure);

[0059] The [Fig.9] is a 3D diagram of the vertical load over the entire span of the square roof structure;

[0060] FIG. 10 is the result of the optimization of the square roof structure composed of 6 different types of modules ([Fig. 10a] is the top view of the optimization results, [Fig. 10b] is the axonometric view of the optimization results, and [Fig. 10c] is the diagram of the 6 different types of modules).

[0061]

[0062] DETAILED STATEMENT OF THE METHOD OF IMPLEMENTATION

[0063] The present invention is described in detail below in connection with the embodiments. The following description of the embodiments is solely for the purpose of facilitating understanding of the present invention. It is understood that a person skilled in the art may make modifications without departing from the technical principle of the present invention, which are included within the scope of the present invention.

[0064] Embodiment I

[0065] In one embodiment, the optimized design and manufacturing process for a three-dimensional truss based on a relaxed modular constraint comprises the following steps:

[0066] SI: Optimization of the initial design layout: As shown in [Fig.2a] to [Fig.2d], in the SI step, the main steps include S 1.1 defining the design domain and boundary conditions as shown in [Fig.2a], S 1.2 discretizing the design domain in the form of a grid of nodes and constructing a grid of nodes including all possible connections between the nodes, as shown in [Fig.2b]; S 1.3 identifying the optimized structure of the subset from the basic structure, as shown in [Fig.2c]; S 1.4 designing variables based on the coordinates of the nodes and using geometric optimization to obtain reasonable optimization results, as shown in [Fig.2d].

[0067] At the SI step, without taking into account the modularity requirement, expressions (1) to (2) are used to perform the layout optimization of the initial design in order to to obtain the initial solution of the layout optimization, and the initial solution is used as a strict lower bound; the objective function corresponding to the design objective of minimizing the total volume of all the truss rods is as follows:

[0068] [Math.l] minV = I ( x, y ) T a 1 a.qjiy \ )

[0069] The expression of the constraints is as follows:

[0070] [Math.2] ' B(x,y)q = f ' -(jca< q< ata > a> 0

[0071] where: V is a total volume of all the rods of the truss, l(x, y ) is a length vector of the rod, a is a surface area vector of the rod, B(x, y ) is an equilibrium matrix, *1 is an internal force vector of the rod, f is a load vector of a node, and are allowable compressive and tensile strengths of the rod, respectively x= [xlr X2, ..., Xj] T and y = [yf y^ ..., y ] T are an x ​​coordinate vector of the node and a Y coordinate vector of the node, respectively, and1 is the number of nodes.

[0072] The three constraints of expression (2) represent a force equilibrium expression, a rod force constraint and a non-negative rod surface constraint, respectively; the design variables are the rod surface vector a, the internal rod force vector 9 and the coordinates x' ¥, B(x, y) and I(X, y) are the matrices and vectors generated as a function of the rod topology, respectively, and f are the constant vectors corresponding to the actual working conditions, and are all the constants corresponding to the actual working conditions.

[0073] S2: Optimization of layout of a modular design: take into account the modular requirements, and perform iterations, each comprising two main steps, in order to refine the initial solution of the layout optimization obtained in step SI into a solution of optimization of a modular design of the layout optimization;

[0074] S2.1: Identification of module layout by data grouping: resolution of the module layout identified in the data grouping in expression (3); use of the data grouping to examine the structural layout to identify relevant module layouts; the Data clustering is an unsupervised learning algorithm that divides objects in a dataset into subgroups based on their similarity, quantified by Euclidean distance, and is expressed as follows:

[0075] [Math.3] (3)

[0076] where: S = {Sp S2, • ••, Sp} is a grouped data set, is the 0th data grouping, P is the total number of data groupings, i.e., the number of module types in the optimization problem; C is a data point belonging to S¢; p — is a center of mass of and | is the number of corresponding data points;

[0077] S2.2: Design of relaxed modular constraints: evolving the solution initial towards a more modular design by using a defined arrangement of modules and re-optimizing the structure by applying relaxed modular constraints;

[0078] S3: geometric optimization: perform a geometric optimization post-processing on a layout optimization result in order to obtain a reasonable and efficient optimization result;

[0079] S4: 3D printing manufacturing and integral assembly: carry out 3D modeling, cutting and generating printing paths for each of the multiple modular units of the optimized model, carry out 3D printing manufacturing and perform the integrated assembly between the modular units to manufacture the optimized structure.

[0080] Embodiment II

[0081] In another embodiment, embodiment II proposes, based on embodiment I, a more specific method for optimizing the design and manufacture of 3D farms based on relaxed modularity constraints, at step S2:

[0082] As shown in FIG. 3a to 3c, in step S2.1, extract a modular layout from the existing structure using a data grouping algorithm, consisting mainly of: S2.1.1: defining a design domain and boundary conditions, as shown in FIG. 3a; S2.1.1: taking a volume of a region as the data to be grouped, namely Ç = vs in formula (3), in order to obtain the optimal modular layout, vs being a volume of the region, as shown in [Fig. 3b]; S2.1.3: solving the linear programming problem in order to obtain a corresponding modular optimization structure after reoptimization, as shown in [Fig. 3c], and solving the expression of the strict modular constraint optimization problem, as shown in expressions (4) to (5), namely a nominal lower bound solution; in the embodiment, a cantilever beam is taken as an example for the description;

[0083] The objective function is as follows:

[0084] [Math.4] minV = I(xy)Ta 4 a,qA!a^,y \ /

[0085] The expression of the constraints is as follows:

[0086] [Math.5] 1 B(x,y)q = f -aca <q< ata ' a> 0 5 VïG{l,2, !

[0087] where: tj is a binary constant representing the number of the Jeme module type in each modular space, which reflects whether the corresponding module type is in an activated state; P is the number of module types, n is the number of units; Anij is an optional region of the stem unit in the Jeme module;

[0088] The data grouping algorithm can lead to suboptimal solutions and is therefore defined in expression (3), with the aim of determining the optimal arrangement of modules with a nominally lower solution.

[0089] S2.2: The main step of relaxing modular constraints, such as indicated in FIG. 4a to 4d, includes: S2.2.1: establishing the given structures of the different module types, as shown in FIG. 4a; S2.2.2: establishing unit-based modular constraints to ensure that the internal structures of module spaces belonging to the same module type are all identical, for example, the same structures of I, II, and III in FIG. 4a, whose module space structure is identical to that of the module space in FIG. 4a. The specific scheme of this module structure is illustrated in FIG. 4b; S2.2.3: dividing the module space into dxd subregions, and constraining the volume of the subregions, as illustrated in FIG. 4c; S2.2.4: When the value of d is sufficiently large, region-based modularity constraints tend to converge towards the results of unit-based modularity constraints; thus, choosing a relatively small value of d is equivalent to relaxed modularity constraints for region-based modularity constraints ([Fig.4d]); the expressions for the relaxed modularity constraints are presented in expressions (6) to (7) to replace the fourth expression of expression (5).

[0090] [Math.6] Vsik^Vtü^^ keHj,b= 1,2, ....d2 (6)

[0091] [Math.7] vslkfi) = ^in&C]kbak^km (^)

[0092] where: vs,(k,b} is a structural volume of the bicmc subregion in the Ath modular space, vt[jJi) is a total volume of the Ath modular region of the Jth module type; Hj is a set of indices of the modular space when the Jth module type is adopted; is the bicmc subregion in the ith modular space; ^k^n and are a cross-section and a length of the rod unit in the bth subregion, respectively, and 212 is the rod number;

[0093] During the optimization process, the modular constraints can be effectively strengthened by systematically increasing the value of d; however, increasing the value of d can also lead to discrete jumps in the subregion; these sudden jumps cause significant changes between iterations, which can lead to a convergence problem; in order to resolve this convergence problem and ensure a smooth transition between iterations, the constraints in expression (6) are modified by means of the more gradual constraint in expression (8).

[0094] [Math. 8] ...,d2 (8)

[0095] where: r is an influencing factor, 0 < r < 1, when r = 1, this means that the constraint expression (6) is completely eliminated, and when r = 0, this means that the constraint expression (6) is completely applied, namely the stricter modular constraints; throughout the iteration, the value of r gradually decreases from about 1 to 0, which allows stricter modular constraints to be applied.

[0096] In step S2.2, the expression for the optimization problem of relaxed modular constraints is solved, and the objective function is as follows:

[0097] [Math.9] minV = l(x, y ) Ta |9j a, q, vt, vs, x, y J \ J

[0098] The expression of the constraints is as follows:

[0099] [Math. 10] 1 B(x,y)q = f - <jca < q < ata , a>0 10 ( 1 -r) < vsikih}< vtm k&Hj,b= 1,2.....d2 ( vs{k,b)= hak^km

[0100] in which the expression of the constraints (10) is composed of the first 3 formulas of expression (5), expression (7) and expression (8).

[0101] Furthermore, the adoption of an improved iterative implementation strategy between step S2.1 and step S2.2, in order to improve the final result of the optimization, namely: at the end of step S2.1, when vf — |a nüse is updated with the arrangement of the modules, then the implementation of step S2.2 in order to solve the optimization problem of the relaxed modular constraints; when > yÇ-l, the direct implementation of step S2.2 in order to solve the optimization problem of the relaxed modular constraints; where: is a volume of the optimized modular structure, and which is solved using expression (5); is the number of iterations, and ^max is the maximum number of iterations defined.

[0102] Step S3 consists of: performing a geometric optimization post-processing on a result of the layout optimization in order to obtain a reasonable and efficient optimization result;

[0103] Step S4 specifically consists of extracting the structural information of the modular unit according to the results of the optimization, the structural information including the mode of the modular unit, the position of the modular unit, the connection of the modular unit and the dimensions of the cross section of the rod of the modular unit; after the assembly of the rod and the processing of the generation of nodes of the modular unit, the establishment of a 3D solid model then the multiple modular units of the solid model are cut and printing paths are generated respectively for 3D printing and manufacturing; finally, connections are established between the modular units for the integrated assembly in order to manufacture the optimized structure.

[0104] It should be noted that parts of this embodiment which are identical or similar to the first embodiment may be cross-referenced and will not be repeated in this application.

[0105] Embodiment III

[0106] In another embodiment, embodiment III is proposed based on embodiments I and II. It consists of optimizing the design and the fabrication of a simply supported bridge using the results of the layout optimization of the initial design of step SI and the layout optimization of the modular design of step S2 of this process of optimizing the design and fabrication of a 3D truss based on the relaxation of modular constraints.

[0107] As shown in FIG. 5, the semi-structure of this simply supported bridge is taken symmetrically for the optimal design, i.e. the design domain 5 m x 2 m is taken, the vertical load F = 0.5 N is applied in the lower right corner of the design domain, the module size is 0.5 m x 0.5 m, the number of module types P = 4, and the module complexity is 4 x 4; the results of the optimization at each step are unfolded to the actual size symmetrically; the changes in the structure in the optimization process are shown in FIG. 6; and FIG. 7 shows the changes in the volume of the structure, the variable d and the variable r during the iteration process.

[0108] First, the layout optimization of the initial design in the SI step is carried out in accordance with expressions (1) to (2), and the results of the optimization are shown in the upper left corner of [Fig.6];

[0109] Next, in the data grouping to identify the modular arrangement in step S2.1, the data from the unit region optimized by the layout of the initial design in [Fig.6] are used to perform the data grouping in accordance with expression (3), which lays the basis for the development of the preliminary modular structure;

[0110] Next, by solving the strict modular constraint optimization expressions (expressions (4) to (5), obtain the module layout optimization results, as shown in the upper right corner of [Fig.6];

[0111] At each iteration, apply the optimization expressions (9) to (10) of the design of the constraints of the soft modulus S2.2, and obtain the results of the intermediate optimization, as shown on the left side of rows 2 to 4 of [Fig.6]; as the optimization progresses, the relaxation decreases, and the results of the intermediate optimization tend towards the modular structure;

[0112] Consequently, update the arrangement of the modules, as shown on the right side of lines 2-4 in FIG. 6, which leads to a reduction in the volume of the corresponding modular structure, as shown in FIG. 7; in the embodiment, the iterative process ends at the last iteration, at which d = 3, r = 0.4 and the optimized volume is 25.04 x 10-6 m3;

[0113] Finally, the structure is rationalized by geometric optimization, which gives the results in the lower left corner of [Fig.6]; by simplifying the internal structure of each type of module and removing the unconstrained modules, the volume of the structure has been further reduced to 23.00 x 10-6 m3.

[0114] The results of the two-step optimization are shown in the lower right corner of [Fig. 6]. In comparison, the optimization results of the patented process correspond to a reduction in the volume of the structure of approximately 2.2%, and only 53 s of CPU computation time are required, whereas the two-step optimization process takes 10,951 s. Therefore, the CPU computation time of the patented process has been reduced by 99.50%, and the computational efficiency has been significantly improved.

[0115] Fig. 7 shows the changes in the volume of the modular structure throughout the selection process; with the exception of the fourth iteration, most of the iterations produce a volume of structure identical or improved compared to the results of the previous steps; after six iterations, the arrangement of the modules and the volume of the structure change less, which indicates that the algorithm has converged.

[0116] Embodiment IV

[0117] In another embodiment, embodiment IV proposes, based on embodiments I and II, the application of the optimization method for the design and manufacture of a three-dimensional truss based on the released modular constraints to a three-dimensional truss model of a square roof covering under four-sided support conditions.

[0118] As shown in [Fig. 8a] and [Fig. 8b], the optimization is performed for a square roof truss structure with a span of 60 m. A simplified analysis is carried out by considering one-quarter of the structure based on symmetry. The full-scale roof structure consists of a 12 x 12 x 2 module grid using six different module types, each with a complexity of 3 x 3 x 3. Supports are placed at 10 m intervals along the four boundaries of the structure. Vertical loads were applied at each node on the top surface of the structure, i.e., full-span loads, to accurately simulate the action of the gravity load G, as shown in [Fig. 9].

[0119] The optimized results of the patented process, shown in [Fig. 10a] to [Fig. 10c], are as follows: the optimized volume of the structure with 6 different module types in [Fig. 10c] is 5,462 x 10⁻⁶ m³ under the full-span load condition, and the optimized solution time is 1,289 s. As a comparative example, 1 module type was used to solve the structure, which corresponds to an optimized volume of 8,614 x 10⁻⁶ m³. The results show that by increasing the number of module types from 1 to 6, a maximum volume reduction of 36.5% can be achieved.

[0120] According to embodiments III and IV, in the optimized design and manufacturing process of a three-dimensional truss based on a relaxed modular constraint according to the present invention, based on the mathematical model For truss layout optimization, a fast and efficient solution based on relaxed modular constraints is achieved through an iterative process involving data grouping to identify module layouts. Modular repeatability and structural regularity of the optimization results are achieved by defining relaxed modular constraints for several module types. Computational efficiency is significantly improved with minimal impact on the final optimized structure. The design of the 3D-printed optimization and the fabrication of integrated assemblies for the optimized three-dimensional truss structure are carried out through 3D modeling, modular slicing of the modular structure, print path generation, and integrated assembly production. The method of the present invention has proven effective after practical verification.

[0121] Each embodiment of this description is described progressively, and each embodiment focuses on the differences with the other embodiments, and each embodiment can refer to the other for the same and similar parts.

Claims

Demands

1. A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint, characterized in that it comprises the following steps: S1: layout optimization of an initial design: performing a layout optimization of an initial design by taking a minimum total volume of all the truss rods as the design objective in order to obtain an initial solution of a layout optimization, and taking the initial solution as a strict lower bound; S2: layout optimization of a modular design: repeating steps S2.1 and S2.2, and refining the initial solution of the layout optimization into a modular design layout optimization solution; S2.1: Identification of module layout by data grouping: adopt data grouping to verify the structural layout and identify the module layout, in order to solve the problem of optimization under strict modular constraints; S2.2: Design of relaxed modular constraints: use the module layout to re-optimize the structure using relaxed modular constraints; S3: Geometric optimization: perform geometric optimization post-processing on a layout optimization result to obtain a reasonable and efficient optimization result; S4: 3D printing fabrication and full assembly: perform 3D printing fabrication of a plurality of optimized modular units, and fully assemble the modular units to fabricate an optimized structure.

2. Optimized design and manufacturing method of a three-dimensional truss based on a relaxed modular constraint according to claim 1, characterized in that, at step SI, an objective function corresponding to the design objective of minimizing the total volume of all the truss rods is as follows: [Math.1] minV = l(x, y)Ta# (1) a,qjc,y a force equilibrium equation, a rod force stress and a non-negative rod surface stress are introduced as stress conditions of formula (1), in which the expression for the stress conditions is as follows: [Math.2] ' B(x,y)q = f - -dca <q<ata # (2) . a> 0 where: V is a total volume of all the rods in the truss, l(x, y) is a rod length vector, a is a rod area vector, B(X, y) is an equilibrium matrix, # is an internal force vector of the rod, f is a load vector of a node, and are the allowable compressive and tensile strengths of the rod, respectively; x x2.....T and y = [yf y2.....yj T are an x ​​coordinate vector of the node and a Y coordinate vector of the node, respectively, and 1 is the number of nodes.

3. Optimized design and manufacturing method of a three-dimensional truss based on a relaxed modular constraint according to claim 1, characterized by, in step SI, first, the definition of a design domain and boundary conditions, then, the discretization of the design domain into a grid of nodes and the construction of a basic structure containing all possible connections between the nodes; the identification of an optimized sub-assembly structure from the basic structure; and the performance of a geometric optimization based on node coordinate design variables.

4. A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint according to claim 1, characterized in that, at step S2.1, the data grouping divides objects from a dataset into different groups based on similarity, the similarity being quantified by a Euclidean distance, the expression being the following: [Math.3] argmmS^SfesJK-^ll2* (3) where: S = { Sp S2, ..., S^, Sp} is a set of grouped data, Sÿ is the (jbth grouping of data, P is the total number of data groupings, i.e., the number of module types in the optimization problem; Ç is a data point belonging to ; p = is a center of mass of and | is the number of corresponding data points; extract a modular layout from the existing structure as a function of the grouping obtained and using a data grouping algorithm: first, define a design domain and boundary conditions, and take a volume of a region for the data to be grouped, i.e. Ç=vs in formula (3), in order to obtain the optimal modular layout, v$ being a volume of the region;and finally, solve the linear programming problem in order to obtain a corresponding modular optimization structure after re-optimization, and solve the strict modular optimization problem, namely a nominal lower bound solution.

5. A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint according to claim 4, characterized in that, at step S2.1, the expression for the strict modular constraint optimization problem is solved, and the objective function is as follows: [Math.4] minV = l(x, y)Ta# (4) a,qAm^,y the expression for the constraints is as follows: [Math.5] ' B(x,y)q = f - has c has <q< a t has 1 a>0 # (5) where: tj is a binary constant representing the number of the Jeme module type in each modular space, which reflects whether the corresponding module type is in an activated state; P is the number of module types, n is the number of units; Amj is an optional region of the stem unit in the jth module.

6. A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint according to claim 5, characterized by, in step S2.2, defining given structures of different types of modules; defining modular constraints based on units as relaxed modular constraints, and ensuring that internal structures of module spaces of the same module type are the same; dividing the module space into dxd subregions, each subregion having a corresponding structure, and limiting a volume of the subregion, the expressions being as follows: [Math.6] = vk GH j, b = 1,2, ..., d 2 # ( 6 ) [Math.7] vs£k,b)= ,ak^k.iii # (7 ) where: vsik,b) is a structural volume of the Same subregion in the Same modular space, is a total volume of the bith modular region of the Jth module type; Hj is a set of indices of the modular space when the Jth module type is adopted; is the bith subregion in the Same modular space; &k,m and 7^. are a cross-section and a length of the rod unit in the Same subregion, respectively, and m is the rod number; for a sufficiently large value of d, modular constraints based on regions also converge to modular constraints based on units; for a relatively small value of d, modular constraints based on regions are also equivalent to relaxed modular constraints, whereby the fourth formula of expression (5) is replaced by expression (6) and expression (7), in order to obtain the design expression for relaxed modular constraints.

7. A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint according to claim 6, characterized in that, at step S2.2, the modular constraints can be reinforced by systematically increasing the value of d; to resolve the convergence problem caused by a discrete jump in the subregion due to the increase in the value of d, expression (6) is modified into expression (8) as follows: [Math.8] k&Hj,b= 1,2, (8) where: r is an influencing factor, 0 < r < 1, when r = 1 it means that constraint expression (6) is completely eliminated, and when r = 0 it means that constraint expression (6) is completely applied; throughout the iteration, the value of r gradually decreases from about 1 to 0.

8. Optimized design and manufacturing method of a three-dimensional truss based on a relaxed modular constraint according to claim 7, characterized in that, at step S2.2, the expression of the relaxed modular constraint optimization problem is solved, and the objective function is as follows: [Math.9] minV = l(x,y) T a# (9) a,q,vf,vs^,y The expression of the constraints is as follows:

9. [Math. 10] 1 B(x,y)q = f - acaata । a-° #(10) (1 - r) < vs[kj3) < w V ke Hj, b = 1,2, ..., d ! vsikJS) ~ in which the expression of the constraints (10) is composed of the first 3 formulas of expression (5), expression (7) and expression (8). A method for the optimized design and manufacture of a three-dimensional truss based on a relaxed modular constraint according to claim 5, characterized by, in step S2, the adoption of an improved iterative implementation strategy between steps S2.1 and S2.2, in order to improve the final result of the optimization, namely: at the end of step S2.1, when vf — |a update of the module layout, then the implementation of step S2.2 in order to solve the problem of optimizing the relaxed modular constraints; when > ^-1, the direct implementation of step S2.2 in order to solve the problem of optimizing the relaxed modular constraints; where: VÇ is a volume of the optimized modular structure, and which is solved using expression (5); is the number of iterations, and ^max is the maximum number of iterations defined.

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