Study on Grid Form Finding and Curvature Optimization of Elastic Gridshell Members

doi:10.3969/j.issn.1000-0232.2024.08.005

Abstract

Abstract: The development of dynamic computation and simulation software provides more powerful tools for the mesh design of elastic gridshells. However, current studies only superficially consider how to increase the fitting accuracy of gridshells and reference curved surfaces, and how to solve the contradiction between grid curvature optimization and the accuracy of network fitting surfaces. Based on extending and improving the compass method and numerical simulation methods, an equilateral meshing technique based on the UV structural line of NURBS surface was proposed to address problems of guidance on curve selection and simulation accuracy in the compass method. Numerical simulation optimization of the solved equilateral grids was conducted, and the iterative optimization algorithm reduced errors brought by physical simulation. Moreover, generation efficiency and fitting accuracy in elastic gridshell design were improved simultaneously.
　　A catenary mesh surface was established as the reference surface for form-finding gridshells. Meshing and optimization were performed on the reference surface. Equilateral grids along different directions could be gained by adjusting the surface's UV directions using the Rhino&Grasshopper parametric design tool to meet requirements on grid uniformity and curvature that adapt to different surface morphological divisions. During grid curvature optimization based on simulating motion constraints, the reference surface was rebuilt by using the grid sides after curvature optimization as the structural lines of the surface to address errors. Equilateral meshing was performed again on the new reference surface. Using iterative optimization prevents excessive differences between reference grids and optimized grids during surface rebuilding. To further verify the necessity of the proposed grid curvature optimization method, the structural finite element analysis method was applied to evaluate the structural performances of elastic grid shells before and after the curvature optimization.
　　Based on the typical cases of complicated gridshell application, the double-vault gridshell model and cross-barrel elastic gridshell model, which have largely consistent scales, were built. This method assessed and optimized the curvature of the heterotropic equilateral grids of the built multi-vault elastic gridshells and the multidirectional barrel elastic gridshells. The maximum curvature of grids before optimization were 0.40m-1 and 0.66m-1, which were predominantly near the main curvature line. After optimization of the grid curvature, the maximum curvatures decrease by 37.5% and 19.7% to 0.25m-1 and 0.53m-1, respectively. In the structural performance analysis of elastic gridshell, the structural stability was measured by buckling displacement of the structure. Analysis results indicate that the structural performance of elastic gridshell after curvature optimization under similar architectural morphology is somewhat improved. For example, the cross-barrel gridshells after curvature optimization are feasible for GFRP materials.
　　The traditional encompass method for equilateral grid division based on a parametric design platform was improved, and an equilateral meshing method of gridshells based on the UV structure of the reference surface was proposed, which increased grid generation operation efficiency and controllability of members. Moreover, the optimization procedures of the iterative generation of a reference surface and equilateral grids were proposed during the grid curvature process based on physical simulation. It effectively controls the grid deformation error produced by simulation. Research results provide a higher degree of freedom and feasibility for subsequent construction of elastic gridshells.

Key words: elastic gridshell, equilateral meshing, grid curvature optimization

摘要： 对传统弹性网壳划分等边网格的圆规法进行改进，提出基于参考曲面UV参数结构的网壳等边网格划分方法；提高了杆件网格生成运算效率和应对复杂曲面的适应性性。同时，在基于物理模拟进行杆件曲率过程中，通过参考曲面和等边网格的迭代生成与优化，有效控制模拟产生的网格形变误差。在此基础上对几种常用弹性网壳材料的结构有限元分析，得出经过曲率优化的弹性网壳结构性能具有显著提升，为后续弹性网壳的建造提供更高的自由度和可行性。

关键词: 弹性网壳, 等边网格划分, 网格曲率优化

CLC Number:

TU201.4

MA Xiongwei, KONG Liming. Study on Grid Form Finding and Curvature Optimization of Elastic Gridshell Members[J]. South Architecture, 2024, 0(8): 41-48.

马雄伟, 孔黎明. 弹性网壳杆件网格找形及曲率优化设计研究*[J]. 南方建筑, 2024, 0(8): 41-48.

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