《杆系结构形态创构方法研究.pdf》由会员分享，可在线阅读，更多相关《杆系结构形态创构方法研究.pdf（157页珍藏版）》请在三一文库上搜索。
1、 摘 要 - I - 摘 要 结构形态创构是建筑与结构交叉领域新兴研究方向之一，是从结构分析出 发，寻求多种“良好”建筑形状的理论方法，对建筑与结构设计的进一步发展 有较深的意义。杆系结构类型众多，在实际工程中应用广泛，杆系结构形态创 构方法的研究具有较高的应用价值，有助于建筑形式的多样化。本文以结构优 化理论为基础，考虑建筑空间制约条件，以结构刚度最大化为设计目标，提出 了兼顾形状、拓扑和截面的杆系结构形态创构方法。方法中考虑了程序通用性， 使方法能够用于各种杆系结构的形态创构。本文主要开展以下几个方面工作： 1. 建立了杆系结构的节点调整方法建立了杆系结构的节点调整方法 从应变能和节点坐标
2、的关系出发，推导了节点移动应变能敏感度表达式， 并考虑空间制约条件，得到了受约束节点移动应变能敏感度表达式。详细分析 了节点移动应变能敏感度的特性，提出了根据应变能对节点坐标的敏感程度逐 步调整节点来实现结构刚度最大化的杆系结构形状创构方法。为了提高进化效 率，进一步研究了节点移动方向的修正方法，对杆系结构形状创构方法进行了 改进。研究发现在应该能收敛阶段，节点移动敏感度趋于零，此阶段的结构具 有对初始缺陷不敏感的特点。 2. 提出了兼顾拓扑和形状的杆系结构拓扑形态创构方法提出了兼顾拓扑和形状的杆系结构拓扑形态创构方法 为了评价每个单元在整个结构中抵抗荷载的贡献程度，定义了单元增减应 变能敏感
3、度，并将其作为衡量单元承载效率高低的指标。利用单元增减应变能 敏感度的特性，研究了单元增减的策略，并结合节点调整，提出了兼顾结构拓 扑与形状的创构方法。该方法通过直接地消除低效单元和在高效单元附近增加 单元，实现了结构的拓扑变化，并通过节点调整修正拓扑变化过程中的节点位 置和结构形状。由于单元可增可减，方法的初始结构既可以简单也可复杂，可 灵活选择。在结构形态确定后，在方法中还引入了截面优化，使方法可以兼顾 形状、拓扑和截面，完善了方法。方法适用广泛，能够用于平面及空间中的各 类杆系结构的形态创构。 3. 在杆系结构形态创构方法中考虑了建筑空间制约条件在杆系结构形态创构方法中考虑了建筑空间制约
4、条件 为增强本文方法的实用性，采用 B 样条曲线（曲面）等来表达建筑要求所 提出的空间制约条件，并在应变能敏感度的推导过程中给予反应，使方法所产 生的结构能够满足建筑要求。此外，还利用初始结构对最终结构的影响，在初 始结构确定时以不同的杆件布置手段来体现空间制约条件。由于初始结构是结 构演化的起点，同时也为新杆件生成提供基本的可能空间，对建筑空间制约条 哈尔滨工业大学工学博士学位论文 - II - 件的实现起重要作用。还通过对不同应用场合下的空间制约条件的处理，增强 了方法的实用性，同时也丰富了结构形态创构方法的内容。 4. 研究方法在平面及空间结构中的应用研究方法在平面及空间结构中的应用 为
5、了探讨方法的适用性，对平面及空间结构中的桁架型结构，树状型结构， 桥梁型结构等进行了大量算例应用实践。算例展现了方法广泛的适用性和实用 性。针对不同支座条件，不同初始结构条件、不同创构策略以及不同结构类型 的杆系结构进行形态创构。考察了进化过程中结构形态变化和力学性能变化， 总结了创构策略对结构形态变化的影响和方法的特点。方法所得结构形式具有 以轴力传递荷载的几何特征，结构形式多呈现优美的弧状，这有利于建筑造型 中美学意图的实现。同时，所得结构形式符合力学概念，可为结构力学教育和 结构设计提供参考。 5. 研究并总结了方法所得结构的力学性能研究并总结了方法所得结构的力学性能 从大量算例的力学量
6、的变化可知，兼顾拓扑与形状的杆系结构形态创构方 法可以使结构向刚度提高、弯矩降低的方向演化，最终结构将以轴力为主要传 递荷载方式。方法中的节点调整对结构力学性能的改善贡献较多。对节点调整 前后结构的稳定性进行验算，结果表明调整后结构不仅可提高结构刚度，且可 提高极限承载力和改善初始节点偏差对结构的影响。虽然以应变能作为目标函 数，但可同时改善多项力学性能指标：结构刚度，结构极限承载力，结构力学 性能的稳定性等，这些力学性能在演化过程中具有同时改善的趋势。 文中方法用 Fortran 语言编程实现，用 ANSYS 有限元软件考察了方法所得 结构的一些力学性能。本文还获得了一套杆系结构形态创构程序
7、。 关键词：形态创构；拓扑优化；形状优化；应变能敏感度；杆系结构 Abstract - III - Abstract Structural morphogenesis is a new research direction of the interdiscipline of architecture and structural enginnering. Based on structural analysis, structural morphogenesis methods are a series of thoeries and methods to seek a variety of
8、good architectural shape. This study can promote the development of the architectural and structural design. Framed structures have many types and a wide range of applications in engineering. Therefore, the research on framed structural morphogenesis method has important application value and is hel
9、pful to diversify the architectural forms. Based on the structural optimization theories, this structural morphogenesis method is put forward for the shape, topology and sizing optimizition of framed structures under architectural space constraints aiming to maximize the structural stiffness. The me
10、thod can be applied to the structural morphogenesis of various framed structures. This paper mainly focused out the following tasks: 1. The nodal adjustment method for framed structures The expressions of nodal strain energy sensitivity are derived from the relationship between strain energy and the
11、 nodal coordinates. Moreover, the expressions of strain energy sensitivity of nodes under the spatial constraints were gotten. The shape morphogenesis method of framed structure, which took the maximization of structural stiffness as the design objective, was put forward through gradual nodal adjust
12、ment after the analysis of the properties of nodal strain energy sensitivity. In order to increase the efficiency of the method, the method for amending the direction of nodal shift was studied further and the shape morphogenesis method of framed structure was improved. It was found that the nodal s
13、train energy sensitivity tended to zero in the convergence stage, and then the corresponding structures were less sensitive to the initial defect. 2. topology morphogenesis method of framed strucutres combining shape and topology optimization To evalue the contribution degree of each element in the
14、whole structure to resisting loads, the elemental strain energy sensitivity for addition and elimination was defined and taken as the efficiency index for bearing loads. The topology and shape morphogenesis method of the framed structures including the nodal adjustment was put forward after the stra
15、tegy study of elemental addition and elimination and the analysis of the properties of the elemental strain energy sensitivity. This method realised the topology change through the direct elimination of inefficient elements and addition of new elements near the highly efficient 哈尔滨工业大学工学博士学位论文 - IV
16、- elements and the nodal position and structural shape were amended by the nodal adjustment during the topology change. The initial structure may be simple or complex because the elements may be added or eliminated in this method. After the structural shape was fixed, the size optimization was intro
17、duced to make this morphogenesis method integrate the shape, topology and size optimization. This method can be used for the morphogenesis of all kinds of framed strucutres in plane or space. 3. Architectural space constraints considered in this mehtod To enhance the usefulness of this method, the a
18、rchitectural spatial constraints from the architectural requirements were expressed by B-spline curves and surfaces , etc.,and were reflected in the strain energy sensitivity to make the structures derived form this method meet the architectural requirements. In addtion, the architectural spatial co
19、nstraints were embodied by the intial strucutres which were set through the different layout of rods according to the influence of the initial structure on final structure. Since the initial structure was the starting point of the structural evlotion and provided the basic posssible allowable space
20、for the generation of new rods, the initial strucutres had an important role on the realization of the architectural spatial constraints. This paper perfected the program fuctions of the method in a variety of spatial constraints for different application situations. This further enhanced the practi
21、cality of the method, and also enriched the theory of structural morphology. 4. Application in the plane and spatial structures for this method In order to discuss the applicability fo the method, a number of application examples were carried out such as trusses, tree-like structures, bridges, etc.
22、in the plane and spatial structures. Numerical examples demonstrated the wide applicability and practicality of this method. The morphorgenesis of these structures was about the different support condition, different initial structures, different morphorgenesis strategyies and different structural t
23、ypes. The changes of structural shape and mechanical behaviors in the evolutionary process were investigated to summarize the properties of the method and the inflence of the morphorgenesis strategyies on the change of strucutral shape. The strucutral shape derived from the method had the geometrica
24、l characters which transferred loads to supports mainly by the axis force. These strucutral shapes often appeared beatiful arc shape and this was benificial for the realization of artistic intention of architechtural shape. Moreover, the structural forms derived from this method conformed to mechani
25、cal concepts, which could be provided for the education of structural mechanics and structural design as reference. 5. The summary of mechanical properties of the structures by this method From the change of mechanical quantities in the numerial examples, the topology and shape morphogenesis method
26、of framed structures can make the Abstract - V - structure evolve in the direction of the decline of strain energy and bending moment, and the finial structure would transfer loads with axis force. The nodal adjustment had great contribution to the improvement of structural mechanical behaviors. By
27、checking stability of the structures in the evolutionary process, it was found that the nodal adjustment can not only improve the structural stiffness and ultimate load, but also less influence by the initial nodal defect. This illustrated that the method taking strain energy as the objective functi
28、on can increase the structural rigidity and the structure of ultimate load; Moreover, the structures derived by the method are less sensitive to the initial defect. These mechanical quantities will be improved simaltinously in the optimization process. The proposed method was coded in Fortran langua
29、ge, and finite element commercial software ANSYS was used in the calculation of some structural mechinical behaviors. In addtion, this paper got the program of the morphogenesis of framed strucutres. Keywords: morphogenesis method; topology optimization; shape optimization; strain energy sensitivity
30、; framed structures 哈尔滨工业大学工学博士学位论文 - VI - 目 录 摘 要. I ABSTRACT III 第 1 章 绪 论 .1 1.1 课题背景1 1.1.1 建筑与结构1 1.1.2 结构形态创构与结构优化设计 4 1.1.3 创构新颖杆系结构形态的可能性和必要性.5 1.2 结构形态创构方法的发展现状.8 1.2.1 结构形态创构发展现状 8 1.2.2 优化理论发展现状10 1.3 本文的主要工作及章节概要 15 第 2 章 基础理论 .17 2.1 杆系结构形态创构问题17 2.2 空间制约条件的表达和处理 17 2.2.1 B 样条基函数与 B 样条曲
31、线曲面及其微分18 2.2.2 空间制约条件的处理20 2.3 目标函数的敏感度.21 2.3.1 节点移动应变能敏感度的推导 22 2.3.2 单元增减应变能敏感度的推导 26 2.4 截面优化27 2.5 本章小结28 第 3 章 杆系结构的节点调整方法29 3.1 节点调整的基本思路 .29 3.2 节点调整方法的建立 .30 3.2.1 节点调整的一般表达式的建立 30 3.2.2 不同结构的迭代式31 3.2.3 节点调整方法的步骤32 3.2.4 算例验证33 3.3 节点调整的二阶方法 .34 目 录 - VII - 3.3.1 基本思想34 3.3.2 应用方法35 3.3.3
32、 算例验证37 3.4 节点移动后的结构信息更新 38 3.5 方法的特点40 3.6 本章小结42 第 4 章 兼顾拓扑与形状的杆系结构形态创构方法.44 4.1 基本思路44 4.2 兼顾拓扑与形状的形态创构方法的建立 45 4.2.1 单元直接撤除和增加策略 45 4.2.2 节点调整的作用及实施 47 4.2.3 方法的创构策略及步骤 47 4.3 拓扑变化导致的结构信息更新.50 4.4 杆系结构形态创构方法的特点.50 4.4.1 只拓扑变化的桁架结构形态创构有效性验证.50 4.4.2 初始结构对最终结构形态的影响.52 4.5 本章小结57 第 5 章 方法在平面结构中的应用5
33、8 5.1 桁架型结构58 5.1.1 平面桁架型结构的分类及特点 58 5.1.2 桁架结构形态创构应用方法及算例.59 5.2 框架型结构64 5.2.1 平面框架结构特点64 5.2.2 框架结构形态创构应用方法及算例.65 5.3 树状型结构73 5.3.1 平面树状结构的特点73 5.3.2 树状结构形态创构应用方法及算例.74 5.4 桥梁型结构83 5.4.1 平面桥梁型结构的特点 83 5.4.2 桥梁型结构形态84 5.5 本章小结95 第 6 章 方法在空间结构中的应用96 6.1 树状型结构形态创构 .96 6.1.1 空间树状型结构的创构特点及初始结构确定.96 哈尔滨
34、工业大学工学博士学位论文 - VIII - 6.1.2 空间曲线约束下的树状型结构 97 6.1.3 空间曲面约束下的树状型结构 102 6.2 桥梁型结构形态创构 .107 6.2.1 空间桥梁结构的创构特点 107 6.2.2 单跨空间桥梁结构107 6.2.3 两跨桥梁结构 111 6.3 单层网壳结构拓扑和形状形态创构113 6.3.1 网壳结构的形态创构特点 113 6.3.2 常规曲面网壳结构的拓扑形态创构.113 6.3.3 单层网壳结构的节点移动调整 118 6.4 本章小结126 结 论.127 参考文献.130 攻读博士学位期间发表的论文及其它成果 140 哈尔滨工业大学学
35、位论文原创性声明及使用授权说明.141 致 谢.142 个人简历.144 Contents - IX - Contents Abstract (In Chinese). Abstract (In English).II Chapter 1 Introduction.1 1.1 Background of the subject.1 1.1.1 Architecture and structure .1 1.1.2 Structural morphogenesis and structural optimization .4 1.1.3 The necessity of morphogenesi
36、s of framed structure with new form5 1.2 Developmental of structural morphogenesis methods.8 1.2.1 Structural morphogenesis8 1.2.2 Optimization theories .10 1.3 Main research contents of this subject15 Chapter 2 Basic theories17 2.1 Formulation of morphogenesis of framed structures 17 2.2 Expression
37、 and treatment of spatial constraints17 2.2.1 B-Spline basis functions, surfaces and curves and their derivative.18 2.2.2 Treatment of spatial constraints20 2.3 Sensitivity of objective function .21 2.3.1 The derivation of nodal strain energy sensitivity22 2.3.2 The derivation of elemental strain en
38、ergy sensitivity26 2.4 Size optimization27 2.5 Brief summary28 Chapter 3 Nodal adjustment method for framed structures29 3.1 Abstraction of nodal adjustment method29 3.2 Establishment of nodal adjustment method.30 3.2.1 The general expression of nodal adjustment.30 3.2.2 Iterative for different stru
39、ctures.31 3.2.3 The procedure of nodal adjustment method32 3.2.4 Numerical examples33 3.3 The second-order method for shape adjustment .34 3.3.1 The basic idea.34 3.3.2 The application method35 3.3.3 Numerical examples.37 3.4 Update of structural information after nodal adjustment.38 3.5 Features of
40、 the nodal adjustment method .40 3.6 Brief summary42 哈尔滨工业大学工学博士学位论文 - X - Chapter 4 The structural morphogenesis method combined topology and shape for framed structures 44 4.1 Abstraction of the morphogenesis method44 4.2 Establishment of the morphogenesis method45 4.2.1 The strategy of direct ele
41、mental addition and elimination45 4.2.2 The introduction of nodal adjustment.47 4.2.3 The procedure of morphogenesis method.47 4.3 Update of structural information after topology change.50 4.4 Features of the morphogenesis method .50 4.4.1 The validation of only topology change for truss50 4.4.2 The
42、 influence of initial structure on final structural shape52 4.5 Brief summary57 Chapter 5 The morphogenesis for plane framed structures 58 5.1 Truss-type structures 58 5.1.1 The classification and features of plane truss 58 5.1.2 Numerical examples and application method59 5.2 Frame structures.64 5.
43、2.1 The features of plane fame structures 64 5.2.2 Numerical examples and application method.65 5.3 Tree-like structures73 5.3.1 The features of plane tree-like structures.73 5.3.2 Numerical examples and application method.74 5.4 Bridge-like structures.83 5.4.1 The features of plane bridge-like stru
44、ctures83 5.4.2 Numerical examples and application method.84 5.5 Brief summary96 Chapter 6 The morphogenesis for spatial framed structures 96 6.1 Spatial tree-like structures96 6.1.1 Features and define of initial structures of spatial tree-like structures.96 6.1.2 Numerical examples under spatial cu
45、rves.97 6.1.3 Numerical examples under spatial curved-surfaces102 6.2 Bridge-like structures.107 6.2.1 The features of spatial bridge-like structures107 6.2.2 Numerical example of single span bridge.107 6.2.3 Numerical example of two spans Bridge111 6.3 Bridge-like structures.113 6.3.1 The features
46、of reticulated domes.113 6.3.2 Numerical examples of topology of conventional reticulated domes.113 6.3.3 Numerical examples of shape of reticulated domes118 Contents - XI - 6.4 Brief summary126 Conclusions.127 References.130 Papers published in the period of Ph.D. education.140 Statement of copyrig
47、ht and Letter of authorization.141 Acknowledgements.142 Resume144 第 1 章 绪 论 - 1 - 第 1 章 绪 论 1.1 课题背景 1.1.1 建筑与结构 建筑是人们从事生产、生活、集会等活动的场所，其目的是为人类提供必 要的使用空间。建筑是形式与内容的对立统一体，形式主要包括建筑样式和空 间形式，而内容则主要包括建筑的功能、审美方面的要求和技术手段对这两方 面要求的支持情况1。结构是构成建筑空间的骨架，是承受荷载的主体2,3， 建筑功能的实现离不开结构。结构形态的选择影响建筑的安全、经济、使用、 审美等多方面对建筑的要求，
48、在建筑方案设计阶段起至关重要的作用。 图 1-1 武汉火车站 图 1-2 上海喜马拉雅中心 Fig.1-1 The Wuhan railway station Fig.1-2 The Himalaya Center 建筑与结构设计始终有着密切的联系，长期以来其理论各自独立快速发 展。虽然两者之间存在区别和相对独立性，但两者也具有相互制约相互影响的 方面。合理的结构隐藏着美得多样统一，不应在建筑中被遮蔽，应充分利用合 理结构给予“使用功能”与“视觉效果”的积极影响。要实现建筑合理性与结 构合理性的统一，相互协调，就必须实现建筑与结构的沟通。它不仅仅是建筑 师与结构工程师的沟通，更是现代结构技术与
49、建筑意图的沟通，也是力的传递 路径与建筑功能、建筑美的沟通。 随着结构技术的发展和大跨度空间建筑的广泛应用， 人们逐渐认识到在大 跨空间结构建筑中不论结构遮蔽程度如何，结构都直接决定着建筑的空间形 式，如图 1-1 所示的武汉火车站。结构形状对建筑效果的积极影响逐渐被重视 起来。建筑师和结构设计者都开始从新审视建筑与结构的协调问题，从已发展 的结构技术角度出发，寻求建筑与结构的协调，探讨结构可为建筑效果提供哪 些贡献。遵循结构中的力学规律，因势利导利用结构的合理几何形体来限定人 哈尔滨工业大学工学博士学位论文 - 2 - 们的视觉空间范围，造成新颖的空间形态，是结构技术与建筑发展相适应的现 代建筑表现技巧之一。 这要求建筑师拥有丰富的结构知识和利用结构知识创作 的意愿。考察目前结构形式和建筑形式的关系可知，壳体结构、膜结构、悬索 结构、拱等具有建筑形式与结构形式高度统一的特点。这些结构形式很大程度 上直接决定了建筑形式，这是结构设计者可以广泛发挥作用的场所。然而，通 常的结构形式只是这些结构的简单组合， 往往不能满足人们对建筑美学的不断 追求。随着计算机技术的发展，当前的结构设计分析手段已比较成熟，但是， 寻求合理结构的过程依然是过去以经验为主的方式。 目前结构形态确定的一般过程是：首先，综合分析建筑结构上的各种制约 条件；然后，根据设计意图假定结