Lightweight optimization method of prestress self-balancing tension lattice structure based on buckling dependence

Abstract

The invention discloses a lightweight optimization method of a prestress self-balancing tension lattice structure based on buckling dependence, and relates to the technical field of structural engineering and computational mechanics. Base structure generation and balance analysis: generating a node set by adopting a discretization method according to a design domain, forming a base structure, and establishing a balance matrix based on a geometric topological relation; carrying out dimensionality reduction preprocessing of symmetry driving, carrying out singular value decomposition on the balance matrix, obtaining a self-stress mode matrix, judging a symmetric group, converting a symmetric self-stress mode matrix, obtaining an independent base, and representing a force density vector as a product of the independent base and an independent design variable; and based on LPSO topological optimization, decoding, adaptive component classification, dual buckling stability check, fitness evaluation and convergence judgment are carried out until iteration is terminated. Through a symmetry-driven dimension reduction strategy and a dual buckling constraint mechanism, high-stability lightweight structure design capable of being periodically assembled is realized, and the optimization calculation efficiency is greatly improved.

Description

Technical Field

[0001] This invention relates to the fields of structural engineering and computational mechanics, specifically a lightweight optimization method for prestressed self-balancing tensile lattice structures based on buckling dependence. Background Technology

[0002] Tensile monolithic lattice structures are self-balancing systems composed of compression members (rods) and tension members (cables). They possess extremely high structural efficiency and a superior strength-to-weight ratio, making them promising for applications in various engineering fields. However, existing optimized designs for tensile monolithic lattice structures face three major technical shortcomings that severely restrict their engineering application effectiveness:

[0003] (1) Stability conflict problem is prominent: Structural optimization needs to establish a balance between preventing the overall system from becoming unstable and avoiding buckling of local components. However, traditional optimization methods generally ignore buckling stability constraints, which leads to the optimized structure often failing prematurely due to cable slack or low-order buckling of members when actually under load, making it difficult to meet engineering safety requirements.

[0004] (2) High computational cost and asymmetrical configuration: Existing designs do not make full use of the geometric symmetry of the structure, resulting in a large number of design variables and a surge in computation during the optimization process; at the same time, the generated structural configuration is asymmetrical and cannot meet the geometric continuity requirements of periodic lattice assembly, which is not conducive to modular manufacturing and assembly.

[0005] (3) Existing algorithms have inherent limitations: When using heuristic algorithms such as genetic algorithms for optimization, the computational cost is high and the convergence efficiency is low. Mixed integer linear programming (MILP) is difficult to effectively handle buckling stability constraints and cannot simultaneously take into account optimization efficiency and structural stability.

[0006] Therefore, there is an urgent need for a tensile lattice structure optimization method that can simultaneously take into account geometric symmetry, global / local stability, and computational efficiency. Summary of the Invention

[0007] To address the shortcomings of existing tensile lattice structure optimization designs, such as insufficient stability, high computational cost, asymmetric configuration, and poor algorithm adaptability, this invention provides a lightweight optimization method for prestressed self-balancing tensile lattice structures based on buckling dependence. Through a symmetry-driven dimensionality reduction strategy and a dual buckling constraint mechanism, it achieves a highly stable and periodically assembleable lightweight structure design, which helps to significantly improve the optimization computational efficiency.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a lightweight optimization method for a buckling-dependent prestressed self-balancing tensile lattice structure, comprising the following steps:

[0009] Step 1: Basic structure generation and equilibrium analysis;

[0010] S1.1. Generate a set of nodes using a discretization method based on the preset design domain. Meanwhile, boundaries are selected in the nodes based on actual working conditions;

[0011] S1.2, Connecting Sets All node pairs in the set are used to generate a potential component set. This leads to the construction of a connection matrix describing the connection relationships between nodes and components. This forms the basic structure;

[0012] S1.3. Based on the geometric topological relationships of the base structure, establish the balance matrix. When the base structure is in a self-equilibrium state, it satisfies In the formula, For force density vector, This is the vector of external forces;

[0013] Step 2: Symmetry-driven dimensionality reduction preprocessing;

[0014] S2.1, Regarding the balancing matrix Perform singular value decomposition and solve its null space to obtain the self-stress mode matrix. ;

[0015] S2.2, Regarding the self-stress mode matrix Each row vector Calculate its Euclidean norm, and determine that two components with the same Euclidean norm of row vectors belong to the same symmetric group;

[0016] S2.3, the self-stress mode matrix Convert to symmetric self-stress mode matrix Independent bases are obtained through orthogonal decomposition. ;

[0017] S2.4, force density vector Represented as an independent basis With independent design variables The product;

[0018] Step 3: Topology optimization based on LPSO;

[0019] Initialize the particle swarm, using the linear combination coefficients of the symmetric self-stressed modes as independent design variables. Each particle corresponds to a set of independent design variables. Iterative updates are performed using the LPSO algorithm. During the iteration process:

[0020] S3.1 Decoding: After each update, the independent design variables corresponding to the particles are... Decoding is performed to obtain the force density vector of each component. ;

[0021] S3.2 Adaptive component classification: Based on the force density vector obtained from decoding. Elements Component classification is performed based on numerical characteristics: if If the corresponding component is determined to be a rod; The corresponding component is determined to be a cable; if The corresponding component is determined to be invalid and is removed.

[0022] S3.3, Double buckling stability check, including:

[0023] Global stability constraint verification: Calculate the tangent stiffness matrix of the base structure. In the formula, Here is the material stiffness matrix. For the geometric stiffness matrix generated by prestressing, check the minimum eigenvalue of the tangent stiffness matrix. , must meet Ensure overall structural stability;

[0024] Local stability constraint verification: For the classified rods, the actual axial compressive force must be less than the Euler critical buckling load; for the classified cables, the actual tension must be greater than 0 to prevent relaxation.

[0025] S3.4 Fitness Assessment: Calculate the objective function The goal is to minimize flexibility while introducing a penalty term, expressed as follows: In the formula, For the flexibility term, It is a displacement vector. The penalty weights for global stability constraints. This refers to the quantity that violates the global stability constraints. The penalty weight for local stability constraints, This represents the amount of violation of local stability constraints;

[0026] S3.5 Convergence Judgment: Update the velocity and position of the particle using the local neighborhood topology, and check whether the preset convergence criterion is met. If convergence is not achieved, repeat the iteration. If convergence is achieved, terminate the iteration process.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention first generates the base structure and performs equilibrium analysis, then uses a symmetry-driven preprocessing module to reduce the dimensionality of the design variables, and then enters the LPSO optimization loop. In the loop, the component type is adaptively classified (rod / cable / deletion), and a double buckling constraint check is enforced until convergence, at which point a lightweight tensile lattice structure is output, which can achieve the following advantages:

[0028] 1. Significantly improved computational efficiency: Dimensionality reduction using symmetric self-stressed modes can reduce design variables by approximately 86.7% (e.g., from 153 to a few modes), and computation time can be reduced by more than 60%.

[0029] 2. Enhanced structural stability: The double buckling constraint forces the failure mode to change from low-order cable relaxation to high-order member buckling, which significantly improves the load-bearing capacity of the structure.

[0030] 3. Ensure geometric symmetry: The optimization results naturally satisfy the geometric symmetry requirements of periodic assembly, avoiding chaotic asymmetrical configurations;

[0031] 4. Superior mechanical properties: Compared with traditional trusses, the optimized tensioned integral structure has higher specific stiffness and more uniform force distribution. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method of the present invention;

[0033] Figure 2 This is a schematic diagram of the base structure and its symmetry grouping in the embodiment;

[0034] Figure 3 This is a comparison chart of the optimization convergence process with and without symmetry constraints applied in the embodiments;

[0035] Figure 4 This is a comparison chart of buckling characteristic values ​​with and without buckling constraints in the embodiments;

[0036] Figure 5 This is a comparison diagram of optimized configurations obtained by considering buckling constraints in the embodiments. Detailed Implementation

[0037] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0038] like Figure 1As shown, a lightweight optimization method for prestressed self-balancing tensile lattice structures based on buckling dependence includes the following steps:

[0039] Step 1: Basic structure generation and equilibrium analysis;

[0040] S1.1 Define the design domain and node set: Based on the preset design domain (such as a cuboid, cube, etc.), generate the node set using a discretization method. Ensure the node set The distribution of each node meets the accuracy requirements, while the boundaries are selected among the nodes based on the actual working conditions;

[0041] S1.2 Constructing the base structure and connection matrix: Connection set All node pairs in the set are used to generate a potential component set. This leads to the construction of a connection matrix describing the connection relationships between nodes and components. This forms a highly redundant base structure;

[0042] S1.3, Equilibrium Matrix Construction: Based on the geometric topological relationships of the basis structure, establish the equilibrium matrix. When the base structure is in a self-equilibrium state, it satisfies the following equation:

[0043] (1)

[0044] In the formula, For force density vector, This is the vector of external forces.

[0045] Step 2: Symmetry-driven dimensionality reduction preprocessing;

[0046] S2.1 Solving for the self-stress modal matrix: For the equilibrium matrix... Perform singular value decomposition (SVD) to solve its null space to obtain the self-stress mode matrix. ;

[0047] S2.2 Symmetric Grouping: For the self-stress mode matrix Each row vector Calculate its Euclidean norm. , means as follows:

[0048] (2)

[0049] In the formula, Represents the self-stress mode matrix The first in OK List, Represents the self-stress mode matrix The total number of columns in the middle.

[0050] If the Euclidean norms of the row vectors corresponding to two components are equal, then the two components are determined to belong to the same symmetric group.

[0051] S2.3, Construction of Orthogonal Symmetric Modal Basis: Constructing the self-stressed modal matrix Convert to symmetric self-stress mode matrix Independent bases are obtained through orthogonal decomposition. ;

[0052] S2.4, Definition of Design Variables: The force density vector... Represented as an independent basis With independent design variables The product of, i.e. This allows for a significant reduction in the dimensionality of the design space.

[0053] Step 3: Topology optimization based on LPSO;

[0054] Initialize the particle swarm, using the linear combination coefficients of the symmetric self-stressed modes as independent design variables. Each particle corresponds to a set of independent design variables. Iterative updates are performed using the LPSO algorithm. During the iteration process:

[0055] S3.1 Decoding: After each update, the independent design variables corresponding to the particles are... Decoding is performed to obtain the force density vector of each component. ;

[0056] S3.2 Adaptive component classification: Based on the force density vector obtained from decoding. Elements Component classification is performed based on numerical characteristics: if The corresponding component is determined to be a compression member (Strut); if The corresponding component is determined to be a cable-loaded component; if The corresponding component is determined to be invalid and is removed.

[0057] S3.3, Double buckling stability check, including:

[0058] Global stability constraint verification: Calculate the tangent stiffness matrix of the base structure. Its expression is:

[0059] (3)

[0060] In the formula, Here is the material stiffness matrix. For the geometric stiffness matrix generated by prestressing, check the minimum eigenvalue of the tangent stiffness matrix. , must meet To ensure the overall stability of the structure;

[0061] Local stability constraint verification: For the compression members obtained from the classification, check the Euler critical buckling load. The formula for calculating the Euler critical buckling load is: ,in, The elastic modulus of the material. Let the moment of inertia of the component section be , For the length of the component, the actual axial compressive force must be less than the Euler critical buckling load; for the tensioned cable components obtained from the classification, check their actual tension, which must be greater than 0 to prevent the cable components from slack.

[0062] S3.4 Fitness Assessment: Calculate the objective function The objective function aims to minimize the compliance of the basic structure, while introducing a stability constraint penalty term to guide the algorithm to converge toward a configuration with a high critical load factor. The expression is:

[0063] (4)

[0064] In the formula, For the flexibility term, It is a displacement vector. The penalty weights for global stability constraints. This refers to the quantity that violates the global stability constraints. The penalty weight for local stability constraints, This represents the amount of violation of local stability constraints;

[0065] S3.5 Convergence Judgment: Update the velocity and position of the particles using the local neighborhood topology, and check whether the preset convergence criteria are met (such as the difference between the objective functions of two adjacent iterations being less than a set threshold, the number of iterations reaching a preset upper limit, etc.). If convergence is not achieved, repeat the iteration; if convergence is achieved, terminate the iteration process.

[0066] After iterating through the above methods to meet the convergence criteria, the final component classification results (the positions and parameters of the retained cables and rods) are output, forming an optimized tensioned monolithic lattice structure. This structure naturally satisfies the geometric symmetry requirements and has the characteristics of lightweight, high specific stiffness and stable load-bearing capacity.

[0067] Example

[0068] This embodiment selects a representative two-dimensional planar fish-belly-shaped tensioned monolithic structure as the lightweight design object to verify the effectiveness of the present invention based on symmetry dimensionality reduction and dual buckling constraint optimization. The specific scheme is as follows:

[0069] Combination Figure 2As shown in the figure, part (a) illustrates the initial design domain of the two-dimensional planar fish-belly tensioned monolithic structure, which includes 14 nodes and high-density connections. Part (b) shows the results of automatic grouping by calculating the self-stress modal norm. Components of the same color in the figure indicate that they are grouped into the same design variable group (e.g., components symmetrical about the central axis), which significantly reduces the number of optimization variables (from 91 to 27 groups), ensuring the geometric symmetry of the optimization results.

[0070] 1. Establishment and initialization of the basic structure model: First, define the initial node distribution within the design domain. In this embodiment, the design domain contains 14 nodes.

[0071] Boundary conditions: The nodes on both the left and right sides are set as fixed supports, and all their translational degrees of freedom are constrained.

[0072] Loading condition: A vertically downward external load is applied to the upper chord nodes of the structure. It simulates the stress under actual working conditions.

[0073] Base structure generation: Connect any two nodes to generate a highly redundant base structure, initially containing 91 potential components (connection members). At this point, if the traditional topology optimization method is used, the number of design variables would be 91.

[0074] 2. Symmetry-driven dimensionality reduction: The symmetry-driven dimensionality reduction strategy of this invention is applied to preprocess the base structure:

[0075] Self-stress modal analysis: Equilibrium matrix of the base structure Perform singular value decomposition. Initialize the self-stress mode matrix of the basis structure. The dimension is 91×67, indicating that the structure has 67 independent self-stress modes.

[0076] Symmetric grouping: Calculation of self-stress mode matrix The Euclidean norm of each row vector in the model is calculated. Based on the equality of the norm values, the 91 components are automatically divided into 27 independent symmetric groups. Components in symmetrical positions (such as the upper and lower chords that are symmetrical about the horizontal central axis) are grouped into the same group.

[0077] Dimensionality reduction results: After constructing the symmetric self-stress mode matrix, the number of independent self-stress modes is significantly reduced from 67 to 22. The optimization algorithm only needs to optimize the combination coefficients of these 22 symmetric self-stress modes, rather than directly optimizing the force density of 91 components, which significantly reduces the dimensionality of the design space.

[0078] 3. Material parameters and constraint settings: Set material properties in the optimization model to distinguish the characteristics of cables and rods. Specific parameters are shown in the table below:

[0079]

[0080] Retention rate constraint: Set the component retention rate to 30% to guide the algorithm to find sparse and efficient topologies.

[0081] Double buckling constraint: Enable positive definiteness check of global tangent stiffness matrix ( ) and local Euler buckling examination ( This ensures that the structure always meets the stability requirements during the iteration process.

[0082] 4. Optimization process and result analysis: The Local Particle Swarm Optimization (LPSO) algorithm was used for iterative solution. The optimization results are as follows:

[0083] Convergence efficiency: Compared to the traditional optimization method without symmetry constraints (which takes 17.2 seconds), the method in this embodiment converges in 6.6 seconds, improving computational efficiency by about 61%.

[0084] Topology configuration: The optimization finally yielded a regular tensioned monolithic structure consisting of 6 compression members and 24 tension cables.

[0085] Regularity of configuration: The structure generated in this embodiment has perfect geometric symmetry, which facilitates modular manufacturing and assembly.

[0086] Stability: This configuration is a typical Class-1 tensioned monolithic structure, meaning that the compression members do not contact each other and are completely surrounded and isolated by a continuous cable net, which effectively avoids the occurrence of long compression members and thus improves the overall buckling resistance of the structure.

[0087] Eigenvalue analysis: After double buckling constraint verification, the minimum eigenvalue of the tangent stiffness matrix of the optimized structure is greater than zero, and the axial pressure of all members is lower than its Euler critical buckling load, which verifies the physical feasibility of the structure.

[0088] Combination Figure 3 As shown, the convergence of optimization without applying symmetric constraints and with the symmetric constraints of this invention are illustrated. The results show that the method of this invention converges in about 20 iterations, and the objective function value is lower; compared with the traditional method, the computation time is reduced from 17.28 seconds to 6.67 seconds, and the efficiency is improved by about 61%.

[0089] Combination Figure 4 As shown, to verify the effectiveness of the dual buckling constraint mechanism of the present invention, the buckling characteristic values ​​of the structures obtained by optimization without buckling constraint and optimization with buckling constraint of the present invention were compared.

[0090] Combination Figure 5As shown in the figure, part (a) illustrates the structural topology generated by the optimization algorithm without considering buckling constraints. This structure contains 14 compression members (thick dark blue lines) and 13 tension cables (thin red lines). It can be seen that this configuration exhibits asymmetric and chaotic characteristics, with long compression members spanning multiple nodes. This structure is highly susceptible to low-order buckling or structural displacement, classifying it as an unstable design. Part (b) shows the optimized configuration after employing the dual buckling constraints and symmetry dimensionality reduction strategy of this invention. This structure contains only 6 compression members and 24 tension cables. A significant feature is that all compression members are short and do not contact each other (isolated by a cable net), forming a typical Class-1 tensioned monolithic structure. This configuration not only possesses perfect geometric symmetry but also effectively shortens the calculated length of the members by increasing the number of cables, thereby significantly increasing the critical buckling load of the structure.

[0091] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0092] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A lightweight optimization method for prestressed self-balancing tensile lattice structures based on buckling dependence, characterized in that: Includes the following steps: Step 1: Basic structure generation and equilibrium analysis; S1.

1. Generate a set of nodes using a discretization method based on the preset design domain. Meanwhile, boundaries are selected in the nodes based on actual working conditions; S1.2, Connecting Sets All node pairs are used to generate a set of potential components. This leads to the construction of a connection matrix describing the connection relationships between nodes and components. This forms the basic structure; S1.

3. Based on the geometric topological relationships of the base structure, establish the balance matrix. When the base structure is in a self-equilibrium state, it satisfies In the formula, For force density vector, This is the vector of external forces; Step 2: Symmetry-driven dimensionality reduction preprocessing; S2.1, Regarding the balancing matrix Perform singular value decomposition and solve its null space to obtain the self-stress mode matrix. ; S2.2, Regarding the self-stress mode matrix Each row vector Calculate its Euclidean norm, and determine that two components with the same Euclidean norm of row vectors belong to the same symmetric group; S2.3, the self-stress mode matrix Convert to symmetric self-stress mode matrix Independent basis is obtained through orthogonal decomposition. ; S2.4, force density vector Represented as an independent basis With independent design variables The product; Step 3: Topology optimization based on LPSO; Initialize the particle swarm, using the linear combination coefficients of the symmetric self-stressed modes as independent design variables. Each particle corresponds to a set of independent design variables. Iterative updates are performed using the LPSO algorithm. During the iteration process: S3.1 Decoding: After each update, the independent design variables corresponding to the particles are... Decoding is performed to obtain the force density vector of each component. ; S3.2 Adaptive component classification: Based on the force density vector obtained from decoding. Elements Component classification is performed based on numerical characteristics: if If the corresponding component is determined to be a rod; The corresponding component is determined to be a cable; if The corresponding component is determined to be invalid and is removed. S3.3, Double buckling stability check, including: Global stability constraint verification: Calculate the tangent stiffness matrix of the base structure. In the formula, Here is the material stiffness matrix. For the geometric stiffness matrix generated by prestressing, check the minimum eigenvalue of the tangent stiffness matrix. , must meet Ensure overall structural stability; Local stability constraint verification: For the classified rods, the actual axial compressive force must be less than the Euler critical buckling load; for the classified cables, the actual tension must be greater than 0 to prevent relaxation. S3.4 Fitness Assessment: Calculate the objective function The goal is to minimize flexibility while introducing a penalty term, expressed as follows: In the formula, For the flexibility term, For displacement vectors, The penalty weights for global stability constraints. This refers to the quantity that violates the global stability constraints. The penalty weight for local stability constraints, This represents the amount of violation of local stability constraints; S3.5 Convergence Judgment: Update the velocity and position of the particle using the local neighborhood topology, and check whether the preset convergence criterion is met. If convergence is not achieved, repeat the iteration. If convergence is achieved, terminate the iteration process.

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