A single-connected structure optimization method and system for additive manufacturing technology

Abstract

The present invention belongs to the field of topology optimization design, and specifically relates to a single-connected structure optimization method and system for additive manufacturing technology, comprising the following steps: S1: using a bidirectional progressive structure optimization method to obtain unit density distribution and sensitivity information of the structure to be optimized; S2: using a connected component marking algorithm to determine the connectivity state of the current optimized structure; S21: when there is no closed cavity in the optimized structure, go to S3; S22: when there is a closed cavity in the optimized structure, construct a continuum structure topology optimization model under connectivity constraints, and use an improved A * The algorithm solves the connectivity path with minimum loss, and based on the constituent units of the connectivity path, weakens the sensitivity of the design variables in the current structure to the global minimum, and then goes to S1; S3: determines whether the final result meets the convergence condition requirements; S31: If so, outputs the optimization result and obtains the topology optimization design scheme of the single-connected structure; S32: If not, go to S1.

Description

Technical Field

[0001] The present invention belongs to the field of topology optimization design, and specifically relates to a single-connected structure optimization method and system of additive manufacturing technology. Background Art

[0002] With the rapid development and application of science and technology and intelligent technology, people's demand for products is not only satisfied with their functionality, but also has higher requirements for their appearance and aesthetics. Therefore, the requirements of various companies for products are gradually reflected in short R&D cycles, low production costs, and endless design solutions. In order to minimize production costs, structural optimization has gradually received widespread attention. It is to optimize the design in a systematic and goal-oriented manner, find a structural configuration that saves money and materials while meeting design requirements, and strive to achieve higher structural performance with less raw materials and lower costs. Topology optimization, as an important part of structural optimization, finds the optimal distribution of materials in the conceptual design stage, which provides an important guarantee for the lightweight and safety of product structures. However, the results of topology optimization are often complex and difficult or even impossible to prepare using traditional manufacturing processes.

[0003] Additive manufacturing technology realizes the preparation of structures by adding materials layer by layer, which can realize the free "growth" molding of geometrically complex structures and greatly expand the design space. Therefore, integrating topology optimization with additive manufacturing and developing innovative design technologies for additive manufacturing have broad prospects. However, additive manufacturing is not "free" manufacturing, and its manufacturing process is still subject to process constraints. Among them, connectivity constraints are a more important additive manufacturing constraint, which requires that the structure cannot contain closed holes. For example, for 3D printing technology based on powder materials, it requires that the final design structure does not produce closed cavities to facilitate the cleaning of unmelted powder. Figure 1 The figure shows a schematic diagram of a structure with a closed cavity that cannot be printed using powder-based 3D printing technology without considering connectivity constraints. After topological optimization of the overall structure, powder trapped in the closed cavity cannot be discharged, ultimately affecting the overall structural performance. Therefore, establishing a structural connectivity constraint model and integrating it into topological design to implement topological optimization methods that consider connectivity constraints has received particular attention and research.

[0004] However, connectivity constraints are often related to design variables. The size of the model and the number of meshes directly impact the computational efficiency of topology optimization under connectivity constraints. To achieve more accurate analysis results, the mesh design is often refined during finite element analysis, which exacerbates the difficulty of integrating connectivity constraints into topology optimization methods and significantly increases computational costs. Summary of the Invention

[0005] The present invention provides a method and system for optimizing a single-connected structure using additive manufacturing technology. By determining the connectivity of the optimized structure and then controlling the connectivity of the structure, the influence of connectivity constraints during each iteration of topology optimization can be effectively avoided, thereby reducing the restriction on the initial structure during optimization. * The algorithm's high-efficiency search speed and high-precision path discrimination planning make the calculated connectivity path more accurate and reliable, and improve computational efficiency. It can quickly obtain an optimized design structure that meets connectivity constraints, making it more applicable to engineering projects.

[0006] A method for optimizing a single-connected structure using additive manufacturing technology comprises the following steps:

[0007] S1: Using a bidirectional progressive structural optimization method, the unit density distribution and sensitivity information of the structure to be optimized are obtained;

[0008] S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure;

[0009] S21: When the optimized structure does not have a closed cavity, go to S3;

[0010] S22: When the optimized structure has a closed cavity,

[0011] S221: Use boundary formula to obtain the set of unit cells at the outer boundary of the structure and the set of unit cells at the closed cavity boundary of the structure;

[0012] S222: Constructing a topology optimization model for continuum structures under connectivity constraints;

[0013] S223: Construct weight maps based on unit design variable sensitivity;

[0014] S224: Adopting Improved A * The algorithm solves the connectivity path with minimum loss and extracts the relevant unit design variable information;

[0015] S225: Based on the component units of the connected path, the sensitivity of the design variables in the current structure is weakened to the global minimum, and then the process is transferred to S1;

[0016] S3: Determine whether the final result meets the convergence condition;

[0017] S31: When the final result meets the convergence condition, the optimization result is output and the topology optimization design scheme of the single-connected structure is obtained;

[0018] S32: When the final result does not meet the convergence condition, go to S1.

[0019] By determining the connectivity of the optimized structure and then controlling the structural connectivity, the influence of connectivity constraints in each iteration of topology optimization can be effectively avoided, reducing the restrictions on the initial structure in the optimization. * The algorithm's high-efficiency search speed and high-precision path discrimination planning make the calculated connectivity path more accurate and reliable, and improve computational efficiency. It can quickly obtain an optimized design structure that meets connectivity constraints, making it more applicable to engineering projects.

[0020] Furthermore, in S1, the specific steps of the bidirectional progressive structure optimization method include:

[0021] S11: define the initial design region of the structure to be optimized;

[0022] S12: Determine the appropriate mesh size and mesh the initial design area of ​​the structure;

[0023] S13: Apply load cases and boundary conditions;

[0024] S14: Obtain density distribution and sensitivity information of each unit.

[0025] By using a bidirectional progressive structural optimization method, it is possible to add units to the "high-performance" area of ​​the material, enhance the model shape optimization capability, reduce the maximum stress and stress concentration, make the structural stress distribution uniform, and then find a better force transmission path to obtain a better topological structure.

[0026] Furthermore, in S2, the connected component labeling algorithm extracts density structural units belonging to the same type of connection and indexes them with unique labels. The expression of the label index is:

[0027]

[0028] Where x e is the design variable, x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the empty unit variable value inside the structure, L1 is the entity label, L2 is the empty label, L v For closed cavity labels;

[0029] In the entire design area, the label vector L={L1,L2,L v}.

[0030] By indexing the density structure units with labels, it is convenient to aggregate the structure units of the same type.

[0031] Furthermore, in S221, the boundary formula is expressed as:

[0032]

[0033] Where x is the unit design variable, d is the unit direction vector, and x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the variable value of the empty unit inside the structure, Γ1 is the external boundary of the structure, and Γ2 is the boundary of the cavity inside the structure. Further, in S222, the continuum structure topology optimization model is:

[0034] Minimize: C = F T U

[0035] Subject to:KU=F

[0036]

[0037] g(L)≤g c

[0038] where:x e =x min or x solid

[0039] Where C is the objective function, F is the external force vector, U is the displacement vector, K is the overall stiffness matrix of the structure, ω is the volume fraction, V e is the volume of the e-th unit; V is the initial volume of the structure; g(L) is the total number of tags; g c is the connectivity constraint threshold.

[0040] Furthermore, in said S224, A is improved * The algorithm expression is:

[0041] f IA (n) = g(n) + ε × h IA (n)

[0042] Where, f IA (n) represents the total estimated cost from the current unit n to the target unit, g(n) is the loss function, which represents the actual cost from the current unit n, and h IA (n) is the heuristic function, which represents the estimated cost from the current unit n to the target unit, and ε is the weight coefficient.

[0043] Improved A *The algorithm can fully utilize the efficiency of local search algorithms and the accuracy of global search algorithms. It is suitable for grid models based on topological sensitivity, and can effectively establish connection channels between closed cavities and the outside world. Its high-efficiency search speed and high-precision path discrimination planning make the calculated connection paths more accurate and reliable.

[0044] Furthermore, the improvement A * The heuristic function h of the algorithm IA (n) The expression is:

[0045] h IA =α×X+β×Y+γ×Φ angle

[0046] Where X and Y are distance vectors, Φ angle is the direction vector, and α, β, γ are weight coefficients.

[0047] Improvement A * The heuristic function h of the algorithm LA (n) Improve the algorithm to enhance its applicability and efficiency in topology optimization connectivity design.

[0048] Furthermore, in S224, the solution model expression of the connection path is:

[0049] Find:e p (p=1,2,...,N)

[0050]

[0051] Subject to:e1∈τ in ,e N ∈τ out

[0052] Where, e p is the unit on the path, N is the total number of units on the path, τ in is the set of boundary cells of the closed cavity of the structure, τ out is the set of outer boundary cells of the structure.

[0053] Furthermore, in S3, the expression of the convergence condition is:

[0054]

[0055] Where i is the current iteration step number, and τ is the change difference.

[0056] A system for implementing a single-connected structure optimization method for additive manufacturing technology, comprising:

[0057] Module S1: Use a bidirectional progressive structural optimization method to construct the unit density distribution and sensitivity information of the structure to be optimized;

[0058] Module S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure; for the optimized structure that does not meet the connectivity conditions, a connectivity path solution model from the cavity to the outer boundary is constructed and iterative optimization is performed until the optimized structure meets the connectivity conditions;

[0059] Module S3: Output the structure that meets the connectivity and convergence conditions to obtain the topology optimization design scheme of the single-connected structure.

[0060] The beneficial effects of the present invention are:

[0061] The present invention can effectively avoid the influence of connectivity constraints in each iteration of topology optimization by determining the connectivity of the optimized structure and controlling the structure connectivity, thereby reducing the restriction on the initial structure in the optimization. * The algorithm can fully utilize the efficiency of the local search algorithm and the accuracy of the global search algorithm, and is suitable for grid models based on topological sensitivity, thereby efficiently establishing a connection channel between the closed cavity and the outside world. Its high-efficiency search speed and high-precision path discrimination planning make the calculated connected path more accurate and reliable, and improve the calculation efficiency. It can quickly obtain an optimized design structure that meets the connectivity constraints and has stronger engineering applicability. The present invention can be efficiently applied to fine grid models and provides a new algorithm for solving topological optimization problems under connectivity constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a schematic diagram showing that a structure with a closed cavity cannot be printed using powder material 3D printing technology;

[0063] Figure 2 is a flow chart of the present invention;

[0064] Figure 3 Schematic diagram of the topology optimization design area, boundary and load conditions in the present invention;

[0065] Figure 4 Schematic diagram of free-form topology optimization results;

[0066] Figure 5 Schematic diagram of topology optimization results considering connectivity constraints;

[0067] Figure 6 Traditional path planning and improved A * Schematic diagram of the computational cost of the algorithm's simply connected structure design;

[0068] Figure 7 Schematic diagram of the system of the present invention.

[0069] Reference numerals:

[0070] 1. Powder conveying system; 2. Lifting system; 3. Laser; 4. Roller; 5. Closed cavity; 6. Connecting hole. DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0072] It should be noted that the experimental methods described in the following embodiments are conventional methods unless otherwise specified, and the reagents and materials are commercially available unless otherwise specified. For those of ordinary skill in the art, the specific meanings of the above terms in this application can be understood in specific circumstances.

[0073] Example 1

[0074] Figure 2 The figure shows a single-connected structure optimization method based on additive manufacturing technology. By controlling the connectivity of the structure to be optimized and then judging its connectivity, the influence of connectivity constraints in each iteration of topology optimization can be effectively avoided, thus reducing the restriction on the initial structure in the optimization. * The algorithm's high-efficiency search speed and high-precision path discrimination planning make the calculated connectivity paths more accurate and reliable, and improve computational efficiency. It can quickly obtain an optimized design structure that meets connectivity constraints, making it more applicable to engineering projects. It specifically includes the following steps:

[0075] S1: Using a bidirectional progressive structural optimization method, the unit density distribution and sensitivity information of the structure to be optimized are obtained;

[0076] S11: define the initial design region of the structure to be optimized;

[0077] S12: Determine the appropriate mesh size and mesh the initial design area of ​​the structure;

[0078] S13: Apply load cases and boundary conditions;

[0079] S14: Obtain density distribution and sensitivity information of each unit.

[0080] S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure;

[0081] The connected component labeling algorithm extracts density structural units belonging to the same type of connection and indexes them with unique labels. The expression of the label index is:

[0082]

[0083] Where x e is the design variable, x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the empty unit variable value inside the structure, L1 is the entity label, L2 is the empty label, L v For closed cavity labels;

[0084] In the entire design area, the label vector L={L1,L2,L v}.

[0085] S21: When the optimized structure does not have a closed cavity, go to S3;

[0086] S22: When the optimized structure has a closed cavity,

[0087] S221: Use boundary formula to obtain the set of unit cells at the outer boundary of the structure and the set of unit cells at the closed cavity boundary of the structure;

[0088] The boundary formula is expressed as:

[0089]

[0090] Where x is the unit design variable, d is the unit direction vector, and x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the variable value of the empty cell inside the structure, Γ1 is the external boundary of the structure, and Γ2 is the cavity boundary inside the structure.

[0091] S222: Constructing a topology optimization model for continuum structures under connectivity constraints;

[0092] Combined with the bidirectional progressive structural optimization algorithm, the continuum structure topology optimization model is:

[0093] Minimize: C = F T U

[0094] Subject to:KU=F

[0095]

[0096] g(L)≤g c

[0097] where:x e =x min or x solid

[0098] Where C is the objective function, F is the external force vector, U is the displacement vector, K is the overall stiffness matrix of the structure, ω is the volume fraction, V e is the volume of the e-th unit; V is the initial volume of the structure; g(L) is the total number of tags; g c is the connectivity constraint threshold.

[0099] S223: Based on the continuum topology optimization model, gridding is used to construct a weight map based on the sensitivity of unit design variables;

[0100] S224: Adopting Improved A * The algorithm solves the connectivity path with minimum loss and extracts the relevant unit design variable information;

[0101] Improvement A * The algorithm expression is:

[0102] f IA (n) = g(n) + ε × h IA (n)

[0103] Where, f IA (n) represents the total estimated cost from the current unit n to the target unit, g(n) is the loss function, which represents the actual cost from the current unit n, and h IA (n) is the heuristic function, which represents the estimated cost from the current unit n to the target unit, and ε is the weight coefficient.

[0104] Among them, the improvement A * The heuristic function h of the algorithm IA (n) The expression is:

[0105] h IA =α×X+β×Y+γ×Φ angle

[0106] Where X and Y are distance vectors, Φ angle is the direction vector, and α, β, γ are weight coefficients.

[0107] The solution model expression of the connected path is:

[0108] Find:e p (p=1,2,...,N)

[0109]

[0110] Subject to:e1∈τ in ,eN ∈τ out

[0111] Where, e p is the unit on the path, N is the total number of units on the path, τ in is the set of boundary cells of the closed cavity of the structure, τ out is the set of outer boundary cells of the structure.

[0112] S225: Based on the component units of the connected path, adjust the corresponding design variables in the current optimized structure and go to S1;

[0113] S3: Determine whether the final result meets the convergence condition;

[0114] The expression of the convergence condition is:

[0115]

[0116] Where i is the current iteration step number, and τ is the change difference.

[0117] S31: When the final result meets the convergence condition, the optimization result is output and the topology optimization design scheme of the single-connected structure is obtained;

[0118] S32: When the final result does not meet the convergence condition, go to S1.

[0119] When the structure meets the connectivity condition but does not meet the convergence condition, the bidirectional progressive structural optimization method is re-adopted to redivide the design area of ​​the optimized structure, construct a new density distribution for each structural unit, and then judge the connectivity condition and convergence condition until it can meet both the connectivity condition and the convergence condition.

[0120] A system for implementing a single-connected structure optimization method for additive manufacturing technology, comprising:

[0121] Module S1: Use a bidirectional progressive structural optimization method to construct the unit density distribution and sensitivity information of the structure to be optimized;

[0122] Module S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure; for the optimized structure that does not meet the connectivity conditions, a connectivity path solution model from the cavity to the outer boundary is constructed and iterative optimization is performed until the optimized structure meets the connectivity conditions;

[0123] Module S3: Output the structure that meets the connectivity and convergence conditions to obtain the topology optimization design scheme of the single-connected structure.

[0124] Example 2

[0125] like Figure 3As shown in the figure, the structure to be optimized is a three-dimensional cubic structure with four bottom sections fixed and the top center subjected to a vertical downward concentrated force F. The size of the structure to be optimized is 80 mm × 80 mm × 40 mm. The maximum design area is determined to be 80 mm × 80 mm × 40 mm by the bidirectional progressive structural optimization method, of which the bottom is a non-design area. The structure to be optimized is divided into 40 × 40 × 20 structural units, and the volume fraction is set to 0.3. The variation difference τ of the convergence condition is set to 0.0001.

[0126] Taking minimizing structural flexibility as the objective function, the objective function expression of the continuum structure topology optimization is:

[0127] Minmize: C=F T U

[0128] Where C is the objective function, F is the external force vector, and U is the displacement vector.

[0129] (1) When free-form topology optimization is performed on the structure to be optimized, the constraints of the continuum structure topology optimization model are:

[0130] Subject to: KU=F

[0131]

[0132] where: x e =x min or x solid

[0133] Where K is the overall stiffness matrix of the structure, ω is the volume fraction, V e is the volume of the e-th unit; V is the initial volume of the structure; x e is the design variable.

[0134] like Figure 4 As shown, it is a free-form topologically optimized structure, in which a closed cavity 5 is formed inside.

[0135] (2) When topology optimization is performed on the structure to be optimized under connectivity constraints, the constraints of the continuum structure topology optimization model are:

[0136] Subject to:KU=F

[0137]

[0138] g(L)≤g c

[0139] where:x e =x min or xsolid

[0140] Where K is the overall stiffness matrix of the structure, ω is the volume fraction, V e is the volume of the e-th unit; V is the initial volume of the structure; g(L) is the total number of tags; g c is the connectivity constraint threshold; x e is the design variable.

[0141] like Figure 5 As shown, it is a topologically optimized structure considering connectivity constraints, in which the closed cavity 5 is eliminated and a connecting hole 6 is formed.

[0142] Topology optimization considering connectivity constraints eliminates closed cavities inside the structure while reoptimizing the model under the constraints of connected path units, minimizing the loss of structural performance.

[0143] At the same time Figure 6 As shown, using improved A * Compared with the traditional graph theory method for single-connected structure topology optimization, the algorithm uses less CPU time in the process of solving the model, which greatly improves the model calculation efficiency.

[0144] The above describes in detail the topology optimization design method for a singly connected structure provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above examples is intended only to facilitate understanding of the method and core concepts of the present invention. It should be noted that those skilled in the art may make various improvements and modifications to the present invention without departing from the principles of the present invention, and such improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing a single-connected structure in additive manufacturing technology, characterized in that: The steps include: S1: Using a bidirectional progressive structural optimization method, the unit density distribution and sensitivity information of the structure to be optimized are obtained; S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure; S21: When the optimized structure does not have a closed cavity, go to S3; S22: When the optimized structure has a closed cavity, S221: Use boundary formula to obtain the set of unit cells at the outer boundary of the structure and the set of unit cells at the closed cavity boundary of the structure; S222: Constructing a topology optimization model for continuum structures under connectivity constraints; S223: Construct weight maps based on unit design variable sensitivity; S224: Adopting Improved A * The algorithm solves the connectivity path with minimum loss and extracts the relevant unit design variable information; S225: Based on the component units of the connected path, the sensitivity of the design variables in the current structure is weakened to the global minimum, and then the process is transferred to S1; S3: Determine whether the final result meets the convergence condition; S31: When the final result meets the convergence condition, the optimization result is output and the topology optimization design scheme of the single-connected structure is obtained; S32: When the final result does not meet the convergence condition, go to S1.

2. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S1, the specific steps of the bidirectional progressive structure optimization method include: S11: define the initial design region of the structure to be optimized; S12: Determine the appropriate mesh size and mesh the initial design area of ​​the structure; S13: Apply load cases and boundary conditions; S14: Obtain density distribution and sensitivity information of each unit.

3. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S2, the connected component labeling algorithm extracts structural units belonging to the same type of connection and indexes them with unique labels. The expression of the label index is: Where x e is the design variable, x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the empty unit variable value inside the structure, L1 is the entity label, L2 is the empty label, L v For closed cavity labels; In the entire design area, the label vector L={L1,L2,L v }.

4. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S221, the boundary formula is expressed as: Where x is the unit design variable, d is the unit direction vector, and x solid is the entity element variable value, x min is the value of the empty cell variable outside the structure, x v is the variable value of the empty cell inside the structure, Γ1 is the external boundary of the structure, and Γ2 is the cavity boundary inside the structure.

5. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S222, the continuum structure topology optimization model is: Minmize:C=F T U Subject to:KU=F g(L)≤g c where:x e =x min or x solid Where C is the objective function, F is the external force vector, U is the displacement vector, K is the overall stiffness matrix of the structure, ω is the volume fraction, V e is the volume of the e-th unit; V is the initial volume of the structure; g(L) is the total number of tags; g c is the connectivity constraint threshold.

6. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In the S224, the improvement A * The algorithm expression is: f IA (n)=g(n)+ε×h IA (n) Where, f IA (n) represents the total estimated cost from the current unit n to the target unit, g(n) is the loss function, which represents the actual cost from the current unit n, and h IA (n) is the heuristic function, which represents the estimated cost from the current unit n to the target unit, and ε is the weight coefficient.

7. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 6, wherein: Improvement A * The algorithm's heuristic function h IA (n) The expression is: h IA =α×X+β×Y+γ×Φ angle Where X and Y are distance vectors, Φ angle is the direction vector, and α, β, γ are weight coefficients.

8. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S224, the solution model expression of the connection path is: Find:e p (p=1,2,...,N) Minmize: Subject to:e1∈τ in ,e N ∈τ out Where, e p is the unit on the path, N is the total number of units on the path, τ in is the set of boundary cells of the closed cavity of the structure, τ out is the set of outer boundary cells of the structure.

9. The method for optimizing a single-connected structure using additive manufacturing technology according to claim 1, wherein: In S3, the expression of the convergence condition is: Where i is the current iteration step number, and τ is the change difference.

10. A system for implementing the single-connected structure optimization method of additive manufacturing technology according to claim 1, characterized in that: include: Module S1: Use a bidirectional progressive structural optimization method to construct the unit density distribution and sensitivity information of the structure to be optimized; Module S2: Use the connected component marking algorithm to determine the connectivity status of the current optimized structure; for the optimized structure that does not meet the connectivity conditions, a connectivity path solution model from the cavity to the outer boundary is constructed and iterative optimization is performed until the optimized structure meets the connectivity conditions; Module S3: Output the structure that meets the connectivity and convergence conditions to obtain the topology optimization design scheme of the single-connected structure.

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