哈尔滨工业大学工学硕士学位论文 - I - 摘 要 平面投影为圆形的单层杆系空间结构的优化设计是离散体结构优化设计的一个热点。以往的研究都是在既有的一种或数种单层球面网壳的基础上进行的，以球面曲率半径、结构中的网格数量、杆件截面为优化变量，所得优化结果仍然是具有特定杆件连接方式的某类单层球面网壳。本文创建的优化方法在一定程度上突破了这种局限，对该类结构的优化设计方法做出了新的探索。 本文借鉴桁架结构拓扑优化设计中普遍采用基结构的做法，构造了一种网格划分方式，以其为基础，形成初始杆件布置方案，根据对称性对杆件及节点进行分组，采取对每组节点给定一组竖向可能位置、对每组杆件给定两种状态（布置或不布置）、对杆件可选截面给定一个按截面特性升序排列的截面表的方式，基于遗传算法，分别建立了形状、杆件布置、杆件截面优化方法，并通过算例，验证了形状、杆件布置和杆件截面变量之间的相互影响。 其中，杆件布置优化方法是在处理结构整体性遭到破坏、优化鸿沟以及无效节点上荷载再分配等问题的基础上建立的。结构整体性遭到破坏即是指杆件布置优化过程中，有可能在结构域中出现杆件或杆件群的“孤岛”从而导致结构总体刚度矩阵奇异；优化鸿沟是指从一种不良的杆件布置方式向较优的杆件布置方式进化时要经历一种更不良的杆件布置方式；无效节点是指随杆件布置优化的进行而在结构域中出现的没有杆件以其为端点的“孤点”，对其上荷载的再分配即是将荷载按照一定规则分配到与其相邻的有效节点上。 在以上工作的基础上，建立了同时对形状、杆件布置、杆件截面进行优化的布局优化方法。其中的关键是：用三条染色体分别存储结构的形状、杆件布置、杆件截面信息，并将其定义为一组染色体，制定相关规则，并以成组染色体为单位进行遗传算法相关操作。 应用布局优化方法，分别对有节点制约条件、有孔洞制约条件以及既无节点制约又无孔洞制约条件下的结构优化设计进行研究。节点、孔洞制约条件指结构中某些位置的节点、孔洞必须存在。相关优化结果表明：制约节点的数量和位置、节点和孔洞制约条件的有无都会对优化结果产生影响。 另外，为了提高单层球面网壳结构方案优选的效率，本文编制了优选程序。基于该程序第一部分通过对每种结构方案应用遗传算法进行截面优化所得结果组建的结构数据库，运行该程序的第二部分可以快速地得到一定跨度一定荷载条件下的以结构总质量为评价指标的较优结构方案。 关键词：单层杆系空间结构；优化设计；遗传算法；单层球面网壳；结构优选 哈尔滨工业大学工学硕士学位论文 - II - Abstract Optimal design of single-layer-bars spatial structures with circular planar projection is a hot spot in optimal design of discrete structures. Previous studies on this issue which always take spherical radius of curvature, grid number in structures and sections of bars as optimization variables are all based on one or several kinds of single-layer spherical reticulated shells. The optimal results obtained are still one kind of single-layer spherical reticulated shells which have specific manner of bar-connection. The optimization method established in this thesis overcomes the limitations to a certain extent and makes a new exploration on the optimal design method of this kind structure. This thesis learns from the thought of ground structure method commonly used in the topology optimization of trusses and constructs a new mesh based on which the initial bars-layout scheme forms. Bars and nodes were classified according to symmetry. A set of possible vertical positions to each group of nodes and two types of states (layout or no layout) to each group of bars were given, and a section table was created in which sections were arranged in ascending order according to properties of sections. Based on Genetic Algorithm, shape, bars-layout, sections of bars optimization methods were established. The interaction between the three optimization variables were tested and verified through examples. The bars-layout optimization method was established on the basis of dealing with problems including the destruction of structural integrity, optimization gap and redistribution of load on invalid nodes. Destruction of structural integrity refers to that isolated islands of bars or bars group may appear during optimal design process of bars-layout which will lead to a singular stiffness matrix of structure. Optimization gap refers to that a worse bars-arrangement occurred when a bad bars-arrangement transmitted to a better arrangement. Invalid node refers to node that no bar takes it as endpoint in the optimal layout process. Redistribution of loads on invalid nodes refers to assign these loads to the adjacent nodes according to certain rules. On the basis of the work above, the layout-optimization method was established in this paper which can optimize shape, bars-layout and sections of bars at the same time. The key is: three chromosomes were used to store information of shapes, bars-layout and sections of bars of a structure respectively. These three chromosomes were defined as one group. According to the related rules formulated, genetic algorithm operations were carried out taking a set of chromosomes as a unit. Using layout-optimization method, the optimal design of structures with 哈尔滨工业大学工学硕士学位论文 - III - constraint-conditions of nodes or constraint-conditions of holes or neither constraint-conditions of nodes nor constraint-conditions of holes were studied respectively. Constraint-conditions of nodes or holes refer to some nodes or holes in the structure must exist. Related optimal results show that: the locations and numbers of restricting nodes, the presence or absence of restricting nodes and holes will have impact on the results of optimal design. In addition, in order to improve the efficiency of optimization of single-layer spherical reticulated shell structures, the secondary optimization programs were written. Based on the structure-database, which composed of optimal results obtained in the section optimization of each structure scheme using Genetic Algorithm from the first part of the program, the optimum structure scheme can be obtained, which was evaluated by mass under certain span and loading conditions. Keywords: single-layer-bars spatial structures, optimal design, GA, single-layer spherical reticulated shell, structural optimization哈尔滨工业大学工学硕士学位论文 - IV - 目 录 摘 要 .