自由曲面空间网格结构网格划分、优化及力性能研究

发布时间：2018-10-24 12:07

【摘要】：随着人们对建筑美学的不断追求、计算机辅助设计水平的日益提高以及施工技术的逐步完善,空间网格结构中较为常见的规则曲面造型,如柱面、球面、椭球面,逐渐无法满足日益发展的建筑表现要求。而自由曲面网格结构凭借其新颖独特的造型和强大的视觉表现力,不断应用于剧院商场、体育场馆、交通枢纽等地标性建筑,越来越受到建筑师的青睐。由于自由曲面网格结构造型复杂,富于变化,在传统的规则曲面中采用的杆件布置方法面对这类曲面已经捉襟见肘,因此如何快速高效地为建筑师的曲面提供优质的网格划分方案是该类结构设计的首要问题；同时,网格的均匀性优化和基于力学性能的研究也是自由曲面网格结构设计的关键性问题。本文针对以上问题进行初步研究,并取得了相应成果。网格划分针对建筑师提供的曲面模型进行,在自由曲面形态创建领域,NURBS逐渐成为主流的造型方法。NURBS作为强大的几何设计工具,为任意曲面提供了一种统一的数学表达,并通过控制点、权因子、节点矢量、阶次等信息实现对曲面的形状控制。本文首先介绍NURBS参数化设计的基本原理,并对其各项控制参数的物理意义进行说明。针对NURBS表达的自由曲面,本文提出一种自动化的网格划分方法——自定义单元法。该方法的网格划分在参数域进行,以网格节点为对象,以“代”为整体进行节点推进。首先根据节点的演化规律进行网格单元自定义,在节点推进过程中根据曲面特征进行单元选择生成下代节点,自适应曲面尺寸变化,将每一推进步单元“组装”,建立网格拓扑的参数化表达；采用黎曼度量表征单元节点参数距离,确定节点参数坐标,适应曲面曲率特征；最后,参数网格映射形成空间网格结构。本研究基于MATLAB编制网格划分及可视化源程序,并通过算例验证了自定义单元方法在自由曲面网格划分中的有效性和通用性。自由曲面网格结构设计中,无论是采用人工划分的方式,还是采用自动划分,初始的网格划分方案均较难确保网格的均匀性,往往需要进行进一步的均匀性优化。本文采用Rhinoceros软件平台,以杆长方差最小为优化目标,编制自动化网格均匀性优化程序。该程序将空间曲面网格转化为参数网格,从而对参数域网格节点进行逐个调整,搜索参数节点最优参数坐标,最终实现参数网格优化,得到均匀性更好的空间网格。当前的自由曲面网格设计研究中,更多是从建筑的美学要求和视觉效果出发,对结构的力学合理性研究有待深入。结构的力学性能直接决定了结构的安全性、适用性和耐久性,自由曲面网格结构力学性能的研究同样是自由曲面网格结构设计的关键性问题。本研究基于大型通用有限元分析软件ANSYS,从结构的静力性能、自振特性、稳定性能方面对自由曲面网格结构的力学特性进行研究,力求为实际工程应用提供有益参考。总之,本文针对自由曲面网格结构的网格划分、网格优化和力学性能三个方面进行研究,以期为自由曲面网格结构的设计提供理论指导和技术支持。
[Abstract]:With the continuous pursuit of architectural aesthetics, the increasing of computer-aided design and the gradual improvement of construction technology, the more common rule-surface modeling in spatial grid structure, such as cylindrical surface, spherical surface and ellipsoidal surface, can not meet the development requirement of building performance. With its novel and unique modeling and powerful visual expressive force, the free-form curved grid structure is continuously applied to landmark buildings such as theaters, stadiums and transportation hubs, and is becoming more and more popular by architects. Because the free-surface mesh structure is complex and rich in shape, the bar layout method used in the traditional regular curved surface faces this kind of curved surface. See the elbow, so how to provide a high-quality grid division scheme for the architect's curved surface quickly and efficiently is the primary problem of this kind of structural design; meanwhile, the uniformity optimization of the grid and the research on the mechanical properties are also the key to the structural design of the free-form curved grid. In this paper, a preliminary study on the above problems is made, and the corresponding results are obtained. Results. Grid partition is designed for the curved surface model provided by architects, and NURBS is becoming the mainstream in the field of free surface form creation The NURBS, as a powerful geometric design tool, provides a uniform mathematical expression for any surface and realizes the curved surface through information such as control point, weight factor, node vector, order and so on. In this paper, the basic principle of NURBS parametric design is introduced, and the physical meaning of the control parameters is introduced in this paper. For NURBS expression free surfaces, this paper proposes an automated grid divider The mesh partition of the method is carried out in the parameter field, and the grid node is an object, " Assemble", establish the parametric representation of the grid topology; use the Riemman Measure to characterize the node parameter distance, determine the node parameter coordinate, adapt to the surface curvature feature; and finally, map the parameter grid. In this paper, the grid partition and visual source program are compiled based on MATLAB, and the method of self-defined unit is verified by calculation example in the free-surface mesh division. In the design of grid structure of free-form curved surface, whether manual partition is adopted or automatic partition is adopted, the initial grid division scheme is more difficult to ensure the uniformity of the grid, and it is often necessary. This paper uses the Rhinoceroos software platform to make the minimum variance of the rod as the optimization objective, and the self-adaptive optimization is developed. According to the program, the space curved surface mesh is transformed into a parameter grid, so that the parameter domain grid nodes are adjusted one by one, the optimal parameter coordinates of the parameter nodes are searched, and finally, the parameter grid optimization is realized, In the current free surface mesh design study, more is from the aesthetic requirements and visual effects of the building, The mechanical rationality of the structure is to be studied deeply. The mechanical property of the structure directly determines the safety, applicability and durability of the structure, and the research on the mechanical properties of the free curved grid structure is also free. Based on the large-scale general-purpose finite element analysis software ANSYS, this paper studies the mechanical properties of the free-surface mesh structure from the aspects of static performance, self-vibration characteristics and stability performance of a large-scale general finite element analysis software ANSYS. In summary, this paper studies three aspects of grid partition, grid optimization and mechanical properties of free-surface mesh structure, with a view to providing free-form surface network.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU399

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