Node semi-rigid modeling-based complex curved surface reticulated shell multi-target form optimization method

Abstract

The invention relates to a node semi-rigid modeling-based complex curved surface reticulated shell multi-objective form optimization method. According to the method, through integration of parametric modeling, numerical simulation and a multi-objective optimization algorithm, efficient optimization design of the irregular boundary free-form surface latticed shell structure is achieved. The control point coordinate matrix of the NURBS curved surface is used for generating a geometric model of the complex curved surface reticulated shell, and high-quality grid division is automatically generated; semi-rigid mechanical behaviors of nodes are simulated through combination of a rigid beam and a spring in a numerical model, semi-rigid characteristics of the nodes are integrated into a rod piece unit, and the mechanical performance of the structure is accurately evaluated; and a non-dominated sorting genetic algorithm is adopted, the minimization of the total strain energy of the structure, the minimization of the total weight of the structure and the maximization of the minimum node configuration degree serve as objective functions, and the multi-objective form optimization design of the complex curved surface reticulated shell is completed. The method is suitable for a single-layer latticed shell structure with any node form and any special-shaped contour boundary, and has wide applicability and good transportability.

Description

Technical Field

[0001] This invention relates to the field of structural engineering, specifically to a multi-objective morphological optimization method for complex curved reticulated shells based on semi-rigid node modeling. Background Technology

[0002] Grid shell structures are spatial structures composed of multiple members connected by nodes. Due to their advantages such as large spans, lightweight yet high strength, and diverse shapes, they are widely used in modern architecture. However, the shape of a grid shell structure has a significant impact on its mechanical behavior; its curved surface directly determines the structure's safety and economy. In practical engineering, to meet different usage requirements, grid shell structures often need to possess complex curved surfaces and irregular boundaries.

[0003] Traditional optimization methods for reticulated shell structures primarily focus on a single objective, such as minimizing strain energy to reflect overall stiffness. However, this single-objective optimization approach struggles to meet the diverse needs of modern engineering projects, encompassing structural safety, economy, and load-bearing capacity. In recent years, multi-objective optimization methods have emerged, typically involving objectives such as strain energy, material usage, and displacement; however, they still fall short in optimizing load-bearing capacity.

[0004] Furthermore, existing research on the optimization of reticulated shell structures largely neglects the influence of the semi-rigid characteristics of nodes on the structural mechanical behavior. In reality, the stiffness characteristics of nodes play a significant role in the overall performance of reticulated shell structures. For example, commonly used semi-rigid nodes (such as welded hollow sphere nodes, bolted sphere nodes, and aluminum alloy plate nodes) are widely used in practical engineering. Although their mechanical performance calculation methods have been provided in standards, specifications, and literature, accurately considering node stiffness during the optimization process remains a problem that urgently needs to be solved.

[0005] During the optimization process, the dynamic changes in surface parameters highlight key issues such as freeform surface mesh generation, automatic geometric model generation, and load boundary condition setting. These issues directly affect the feasibility and accuracy of the optimization design. For example, for surfaces with large local curvature, especially at the surface edges, the mesh generation quality may be poor, and even mesh overlap and intersection may occur. These problems have not yet been effectively solved in existing technologies, limiting the development of optimization design for complex curved reticulated shell structures. Summary of the Invention

[0006] This invention aims to overcome the shortcomings of existing technologies and provide a multi-objective morphological optimization method for complex curved reticulated shells based on semi-rigid node modeling. It solves the limitations of traditional optimization methods, the neglect of the influence of node stiffness, the problems of mesh generation and modeling in the optimization process, as well as the applicability and portability of the optimization method.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows: A multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is characterized by: achieving efficient optimization design of irregular boundary free-form reticulated shell structures through the integration of parametric modeling, numerical simulation, and multi-objective optimization algorithms, specifically including: Parametric geometric modeling: The geometric model of complex curved surface shells is generated using the control point coordinate matrix of NURBS surfaces, and high-quality mesh generation is automatically generated by using a mesh optimization method based on inter-particle interaction forces, combined with mesh quality checking and optimization algorithms. Semi-rigid node simulation: In the numerical model, the semi-rigid mechanical behavior of nodes is simulated by combining rigid beams and springs, integrating the semi-rigid characteristics of nodes into the rod elements to accurately evaluate the mechanical performance of the structure. Multi-objective optimization: A non-dominated sorting genetic algorithm is used to complete the multi-objective morphological optimization design of complex curved reticulated shells with the objective functions of minimizing the total strain energy, minimizing the total weight of the structure, and maximizing the minimum node configuration degree.

[0008] The multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is characterized by the following specific steps in parametric geometric modeling: Initialize the control point coordinate matrix to generate a NURBS surface describing the structural morphology, with the following parametric equations: In the formula, S(u, v) represents the geometric coordinates of the points corresponding to parameters u and v on the surface; N i,k (u), N j,k (v) represents the k-th and l-th order B-spline basis functions in the directions u and v; u and v are the parameters in two orthogonal directions in the parameter domain; u i v j Let be the i-th and j-th nodes in the u and v directions, respectively; U = {u0, u1, …, u} m + k + 1 V = {v0, v1, … , v} n + l + 1} are the node vectors that are monotonically non-decreasing in the u and v directions, respectively; P i,j Let w be the geometric coordinates of the control point in the i-th row and j-th column of the control point network; i,j To control point P i,j Corresponding weight factors; A planar mesh of equilateral triangles is generated based on the building surface, trimmed according to the projected contour, and then mapped onto the surface. The mesh is optimized using the interparticle force method, and the meshing parameters are iteratively adjusted using a quality check algorithm until the requirements for rod length uniformity and Jacobian ratio are met.

[0009] The multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is characterized by the following specific steps in the nodal semi-rigid simulation: Develop a program to calculate structural load information and boundary constraints, and output the results to the finite element analysis module; Calculate the mechanical properties of semi-rigid nodes based on the node design scheme, including the moment-rotation relationship of welded hollow sphere nodes and bolted sphere nodes; A rigid beam and spring combination model is adopted at the end of the member, and the elastoplastic behavior in 6 degrees of freedom is defined to establish an overall structural analysis model that considers the stiffness of the nodes.

[0010] The multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is characterized by the following specific steps in the multi-objective optimization: The independent variable is the NURBS surface control point coordinate matrix, the objective function is the minimum nodal configuration, the total strain energy of the structure and the total weight of the structure, and the constraints include displacement limits and stability requirements. The Pareto optimal solution set is generated using the NSGA-II algorithm, and non-dominated solutions are output for engineers to choose from. The objective function can be replaced with displacement, frequency, or other indicators according to project requirements to achieve multi-scenario adaptation.

[0011] The multi-objective morphology optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is characterized by the following steps: The method is applicable to single-layer reticulated shells with a defined morphology. Input the geometric parameters and node types of the existing reticulated shell; The geometric modeling module is called to generate a numerical model, which is then imported into the numerical simulation module for mechanical performance evaluation. By optimizing the solution module and adjusting the mesh generation or nodal stiffness parameters, mesh optimization or local reinforcement design can be achieved.

[0012] The multi-objective morphological optimization method for complex curved reticulated shells based on node semi-rigid modeling is characterized in that the method implements the following functions through a Python extension of Grasshopper: Data transfer: Transfer the control point coordinate matrix from Grasshopper to ANSYS; Mesh quality assessment: Automatically filters low-quality meshes based on indicators such as aspect ratio and interior angles; Dynamic optimization: Iteratively adjust mesh parameters and feed them back to the geometry modeling module to form a closed-loop optimization process.

[0013] The beneficial effects of this invention are as follows: As can be seen from the above technical solution, this application provides a multi-objective morphological optimization method for complex curved reticulated shells based on semi-rigid node modeling. By introducing a multi-objective optimization framework, minimizing the total strain energy of the structure, minimizing the total weight of the structure, and maximizing the minimum node configuration are used as objective functions, which can simultaneously consider the safety, economy, and load-bearing performance of the structure. This multi-objective optimization method not only considers the overall stiffness and mechanical properties of the structure, but also focuses on the economy of material usage and the stability of the structure. Compared with traditional single-objective optimization methods, this invention can provide a more comprehensive and reasonable optimization design scheme, meeting the diverse needs of complex curved reticulated shell structures in modern engineering.

[0014] This invention particularly emphasizes the influence of nodal stiffness on the mechanical behavior of reticulated shell structures. By employing a combination of rigid beams and springs in the numerical model to simulate the mechanical behavior of nodes, the nodal stiffness characteristics are integrated into the member elements, accurately reflecting the actual mechanical properties of the nodes. This method significantly improves the reliability and practicality of the optimization results, avoiding deviations caused by neglecting nodal stiffness. In practical engineering, the stiffness characteristics of nodes play an indispensable role in the overall performance of the structure; this improvement in the invention makes the optimization design more closely aligned with practical application requirements.

[0015] An automated mesh generation method is also proposed. This method improves rod length uniformity through a mesh optimization approach based on interparticle forces, and further enhances mesh quality by introducing mesh quality checking and optimization algorithms. This approach is particularly suitable for mesh generation in areas with large local curvature or at edges, effectively avoiding mesh overlap and intersection issues, ensuring the feasibility and accuracy of the optimization design. Automated mesh generation not only improves modeling efficiency but also reduces human error, providing reliable technical support for the optimization design of complex curved reticulated shell structures.

[0016] By combining parametric modeling techniques with multiple programming languages ​​and analysis software, a complete optimization calculation process is provided. This method is applicable to single-layer reticulated shell structures with arbitrary node forms and irregular contour boundaries. It can be used not only for morphological optimization of single-layer reticulated shells but also for mesh optimization, geometric modeling, and numerical calculation of single-layer reticulated shells with defined shapes. Furthermore, this invention has good portability and can be applied to various other programming languages ​​or analysis software, enabling its widespread application in the design of complex curved reticulated shell structures in civil engineering, demonstrating broad applicability and good versatility.

[0017] This invention significantly improves the efficiency and reliability of the optimization design of complex curved reticulated shell structures through key technologies such as a multi-objective optimization framework, accurate simulation of nodal stiffness, automated mesh generation and optimization, parametric modeling, and joint invocation. These improvements not only enhance the credibility and practicality of the optimization results but also provide an efficient and reliable solution for the design of modern complex curved reticulated shell structures, possessing significant engineering application value. Attached Figure Description

[0018] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is the projection of the boundary contour of the reticulated shell in Embodiment 2 of the present invention; Figure 3 This is the finite element model of the rod that considers the stiffness characteristics of the nodes used in this invention; Figure 4 This is a flowchart of the complex curved reticulated shell modeling analysis and morphological optimization method based on genetic algorithm provided in Embodiment 2 of the present invention; Figure 5 This represents the optimal individual objective function value in Embodiment 2 of the present invention; Figure 6 These are some typical optimization results of Embodiment 2 of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection claimed in this application. Example 1 A multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling is proposed. This method involves the joint invocation of multiple programming languages ​​and analysis software. The main program, based on a non-dominated sorting genetic algorithm, calls Grasshopper and ANSYS to complete structural modeling and computational analysis, integrating them into an overall optimization framework. In addition, Python language is used to extend Grasshopper's functions for data transfer, mesh generation and pruning, mesh quality evaluation and optimization, providing a complete set of optimization calculation processes applicable to free-form reticulated shells with irregular boundaries.

[0020] This invention comprises three modules: geometric modeling, numerical simulation, and optimization solution. The optimization solution serves as the core module, calling upon the geometric modeling and numerical simulation modules to complete the modeling and analysis tasks.

[0021] The specific steps are as follows: Step 1: Input initial conditions to complete the parametric geometric modeling of the reticulated shell structure; Step 1.1: Initialize the control point coordinate matrix and generate the NURBS surface describing the structural morphology. The parametric equations of the NURBS surface are shown below: (1) (2) In the formula, S(u, v) represents the geometric coordinates of the points corresponding to parameters u and v on the surface; N i,k (u), N j,k (v) represents the k-th and l-th order B-spline basis functions in the directions u and v; u and v are the parameters in two orthogonal directions in the parameter domain; u i v j Let be the i-th and j-th nodes in the u and v directions, respectively; U = {u0, u1, …, u} m + k + 1 V = {v0, v1, … , v} n + l + 1} are the node vectors that are monotonically non-decreasing in the u and v directions, respectively; P i,j Let w be the geometric coordinates of the control point in the i-th row and j-th column of the control point network; i,j To control point P i,j The corresponding weighting factor.

[0022] Step 1.2: Based on the building surface of the shell structure, generate an equilateral triangular planar mesh structure larger than the projection range of the building surface; then, based on the projection contour of the surface, trim the equilateral triangular planar mesh according to the relative positional relationship between the triangular mesh and the projection contour; finally, "map" the trimmed mesh onto the building surface. Step 1.3: Use a mesh optimization method based on interparticle forces to perform preliminary mesh optimization. For surfaces with large local curvature, especially at the edges, the mesh quality may be poor, and mesh overlap may even occur. Therefore, a mesh quality check algorithm and an optimization algorithm are introduced. Based on the mesh quality evaluation index, optimal mesh parameters are iteratively searched until the mesh quality meets the requirements. Simultaneously, the structural layout scheme is output. Step 2: Establish a numerical calculation model of the reticulated shell structure that considers the nodal stiffness in order to accurately evaluate the mechanical performance of the structure; Step 2.1: Based on the structural layout and load conditions, develop a program to calculate the load information and boundary constraints of the structure, and output the calculation results for subsequent finite element calculations; Step 2.1: Calculate the mechanical properties of the nodes according to the node design scheme. For commonly used semi-rigid nodes, such as welded hollow sphere nodes, bolted sphere nodes and aluminum alloy plate nodes, the calculation methods for their mechanical properties have been given in various standards, specifications or literature, and will not be repeated here. Step 2.2: Import the structural and load data output from the geometric modeling module, establish a numerical analysis model, and use a combination of rigid beams and springs at the ends of the members to simulate the mechanical behavior of the nodes, thereby establishing an overall structural analysis model that considers the stiffness of the nodes. Customize the elastoplastic behavior of the nodes in the six degrees of freedom as needed. Step 3: Introduce optimization algorithms and integrate the mesh generation method, load calculation method in Step 1 and the numerical model establishment method in Step 2 to complete the multi-objective morphological optimization of complex curved reticulated shells; Step 3.1: Introduce the optimization algorithm and set parameters such as independent variables, objective function, constraints, population size, and genetic generations; among them, the independent variable is the control point coordinate matrix of the NURBS surface describing the structural morphology, and other parameters depend on the specific problem to be solved; Step 3.2: Using the optimization algorithm as the core, integrate structural geometric modeling and numerical analysis methods to complete the optimization iteration task; Step 3.3: Output the optimization results and perform data processing to complete the multi-objective morphological optimization design of complex curved surface spatial shells.

[0023] The method described above is applicable to single-layer reticulated shells with arbitrary node forms and arbitrary irregular contour boundaries. It can be used not only for the morphological optimization of single-layer reticulated shells, but also for the mesh optimization, geometric modeling, and numerical calculation of single-layer reticulated shells with a defined shape.

[0024] Example 2 like Figure 1 As shown: This embodiment is a single-layer reticulated shell with an irregularly shaped boundary free-form surface. All members are circular tubes with a cross-section of Φ245×12. The hollow welded spherical nodes have a diameter of 650 mm and a wall thickness of 18 mm. Q235 steel is used, and the material constitutive model employs a bilinear kinematic hardening model. The boundary of the reticulated shell is a closed, peanut-shaped NURBS curve, as shown below. Figure 2 As shown; five control points are defined in each of the u and v directions, and the morphology of the reticulated shell is optimized by changing the z-coordinate of the control points; The optimization process in this embodiment is based on a multi-objective optimization algorithm. First, a geometric model of a reticulated shell with irregular boundaries is constructed using parametric modeling techniques. Second, the mechanical performance parameters of the hollow welded spherical nodes are calculated, and the node stiffness characteristics are integrated into the member elements. Figure 3A finite element model of a spatial reticulated shell considering the semi-rigid characteristics of its nodes is established. Finally, an intelligent optimization algorithm is used to perform multi-objective optimization of the structural morphology. For the complex curved surface reticulated shell modeling analysis and morphological optimization method based on multi-objective optimization algorithm in this embodiment, see [link to relevant documentation]. Figure 4 .

[0025] After optimization, this embodiment obtained 10 Pareto optimal solutions, such as... Figure 5 As shown. Optimization results indicate a significant correlation among structural performance indices. A decrease in total strain energy implies an increase in overall stiffness, leading to an increasing structural sag. Simultaneously, the structural self-weight and minimum nodal configuration increase synchronously. This relationship reveals the constraints between structural stiffness, load-bearing capacity, and economy in reticulated shell design. Appropriately increasing the structural sag can effectively improve load-bearing performance, but this requires a trade-off in the increased material usage. Among all optimized individuals, Figure 6 The first structure in the design has the smallest weight, the second structure has the smallest strain energy and the largest minimum nodal configuration. The lightweight design performs well in controlling the amount of steel used, while the high stiffness design significantly improves the mechanical properties of the structure, demonstrating the advantages of multi-objective optimization in coordinating contradictory design objectives.

[0026] This invention establishes an automated mesh generation and modeling analysis method for complex curved reticulated shell structures with irregular boundaries. The former employs a mesh optimization method based on inter-particle forces to improve the uniformity of rod lengths and introduces mesh quality checking and optimization algorithms to further enhance mesh quality; the latter can accurately output the load coefficients at each node, establishing geometric and numerical models for structural morphology optimization analysis.

[0027] The proposed multi-objective morphological optimization method for complex curved reticulated shells uses minimum nodal configuration degree, total structural strain energy, and total structural weight as objective functions, balancing structural safety and economy, and is easy for engineers to use. It is worth noting that the objective function selected in this invention is not mandatory; other optimization objectives can be chosen according to project needs.

[0028] This invention targets single-layer reticulated shells with arbitrary node forms and irregularly shaped boundary contours for optimization. It can be used not only for morphological optimization of single-layer reticulated shells, but also for mesh optimization, geometric modeling, and numerical computation of single-layer reticulated shells with a defined shape. This invention provides a complete set of optimization calculation processes and has good portability, making it applicable to various other programming languages ​​or analysis software.

[0029] The above are merely embodiments provided in this application and are not intended to limit this application. Although this application has been described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. However, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A multi-objective morphological optimization method for complex curved reticulated shells based on nodal semi-rigid modeling, characterized in that: By integrating parametric modeling, numerical simulation, and multi-objective optimization algorithms, efficient optimization design of irregular boundary freeform surface reticulated shell structures is achieved, specifically including: Parametric geometric modeling: The geometric model of complex curved surface shells is generated using the control point coordinate matrix of NURBS surfaces, and high-quality mesh generation is automatically generated by using a mesh optimization method based on inter-particle interaction forces, combined with mesh quality checking and optimization algorithms. Semi-rigid node simulation: In the numerical model, the semi-rigid mechanical behavior of nodes is simulated by combining rigid beams and springs, integrating the semi-rigid characteristics of nodes into the rod elements to accurately evaluate the mechanical performance of the structure. Multi-objective optimization: A non-dominated sorting genetic algorithm is used to complete the multi-objective morphological optimization design of complex curved reticulated shells with the objective functions of minimizing the total strain energy, minimizing the total weight of the structure, and maximizing the minimum node configuration degree.

2. The method for multi-objective morphological optimization of complex curved reticulated shells based on node semi-rigid modeling as described in claim 1, characterized in that... The specific steps of parametric geometric modeling include: Initialize the control point coordinate matrix to generate a NURBS surface describing the structural morphology, with the following parametric equations: In the formula, S(u, v) represents the geometric coordinates of the points corresponding to parameters u and v on the surface; N i,k(u)、Nj,k (v) represents the k-th and l-th order B-spline basis functions in the directions u and v; u and v are the parameters in two orthogonal directions in the parameter domain; u i、 v j Let U and V be the i-th and j-th nodes in the u and v directions, respectively; U = {u0, u1, … , um + k + 1}, V = {v0, v1, … , v n + l + 1} Let P be the node vectors that are monotonically non-decreasing in the u and v directions, respectively; i,j Let w be the geometric coordinates of the control point in the i-th row and j-th column of the control point network; i,j To control point P i,j Corresponding weight factors; A planar mesh of equilateral triangles is generated based on the building surface, trimmed according to the projected contour, and then mapped onto the surface. The mesh is optimized using the interparticle force method, and the meshing parameters are iteratively adjusted using a quality check algorithm until the requirements for rod length uniformity and Jacobian ratio are met.

3. The method for multi-objective morphological optimization of complex curved reticulated shells based on node semi-rigid modeling as described in claim 1, characterized in that... The specific steps for simulating semi-rigid nodes include: Develop a program to calculate structural load information and boundary constraints, and output the results to the finite element analysis module; Calculate the mechanical properties of semi-rigid nodes based on the node design scheme, including the moment-rotation relationship of welded hollow sphere nodes and bolted sphere nodes; A rigid beam and spring combination model is adopted at the end of the member, and the elastoplastic behavior in 6 degrees of freedom is defined to establish an overall structural analysis model that considers the stiffness of the nodes.

4. The multi-objective morphological optimization method for complex curved reticulated shells based on node semi-rigid modeling as described in claim 1, characterized in that... The specific steps of multi-objective optimization include: The independent variable is the NURBS surface control point coordinate matrix, the objective function is the minimum nodal configuration, the total strain energy of the structure and the total weight of the structure, and the constraints include displacement limits and stability requirements. The Pareto optimal solution set is generated using the NSGA-II algorithm, and non-dominated solutions are output for engineers to choose from. The objective function can be replaced with displacement, frequency, or other indicators according to project requirements to achieve multi-scenario adaptation.

5. The multi-objective morphological optimization method for complex curved reticulated shells based on node semi-rigid modeling according to claim 1, characterized in that: The method is applicable to single-layer reticulated shells with a defined shape, and the specific steps include: Input the geometric parameters and node types of the existing reticulated shell; The geometric modeling module is called to generate a numerical model, which is then imported into the numerical simulation module for mechanical performance evaluation. By optimizing the solution module and adjusting the mesh generation or nodal stiffness parameters, mesh optimization or local reinforcement design can be achieved.

6. The multi-objective morphological optimization method for complex curved reticulated shells based on node semi-rigid modeling according to claim 1, characterized in that: The method described implements the following functionality by extending Grasshopper with Python: Data transfer: Transfer the control point coordinate matrix from Grasshopper to ANSYS; Mesh quality assessment: Automatically filters low-quality meshes based on indicators such as aspect ratio and interior angles; Dynamic optimization: Iteratively adjust mesh parameters and feed them back to the geometry modeling module to form a closed-loop optimization process.

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