基于B样条理论的自由曲面结构形态创构方法研究

发布时间：2018-02-24 13:52

本文关键词： 自由曲面 B样条建筑边界应变能敏感度　出处：《哈尔滨工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着社会文明的发展,建筑的活动空间在不断的改善和扩充,人们越来越觉得固有的建筑形式选择范围有限,不能满足日益发展的对建筑表现力的要求。自由曲面结构造型美观,具有强烈的视觉冲击效果,能够生成多种多样灵活多变的几何形状来满足建筑设计上的要求。如何建立合理的自由曲面结构形态创构方法,是目前需要解决的主要问题。本文针对在实际工程中可能存在的多种复杂内外建筑边界条件,利用B样条曲线理论,引用Delaunay三角剖分技术对平面设计域进行三角剖分,投影到B样条曲面上,建立了具有复杂设计域的自由曲面初始模型,提出了利用少数关键点来调整曲面形状的自由曲面结构形态创构方法。主要包括以下内容:1.创建自由曲面结构初始模型初始模型的建立是自由曲面结构形态创构的基础,本文基于B样条曲线理论,利用奇次周期参数化B样条曲线,生成多种次数、多条曲线共同组成建筑外边界和内边界,充分满足建筑设计上对于边界造型丰富、内部预留孔洞的要求,在工程实际方面有更强的实用性;2.确定评价目标函数在优化过程中,需要对每一步得到的优化结果进行评价,评价的内容需要综合考虑结构整体受力情况,评价的目标函数与变量之间的关系应该是能够用程序来实现,而且表达式应尽可能简单,提高计算效率。本文采用应变能作为评价指标,应变能能够综合反应结构的整体力学性能,通过对应变能的单目标优化来寻找力学性能合理的结构。在进化过程中,保证结构的整体刚度增大,最终以薄膜内力的方式传递荷载;3.建立结构形态优化方法为了得到合理的结构形态,需要将自由曲面的几何创建方法与结构形态优化算法结合起来,通过对曲面形状决定参数的优化调整,逐步得到造型美观且受力合理的自由曲面。本文首先详细推导了B样条曲面上关键点的应变能敏感度的表达式,给定步长,对曲面上关键点纵坐标在敏感度负梯度方向上进行调整,使得到的最终结构应变能达到较低水平,且敏感度趋于零,此时自由曲面结构达到相对合理的受力状态。利用本文建立的方法得到的自由曲面结构表面光滑连续,无需二次加工,而且只需要计算曲面上关键点的应变能敏感度,计算量小,计算效率高。同时,曲面边界多样,凹凸丰富。该方法不仅仅是更加深入的理论研究,同时具有很高的工程实用性。
[Abstract]:With the development of social civilization and the continuous improvement and expansion of the active space of architecture, people increasingly feel that the scope of choice of inherent architectural forms is limited. Can not meet the growing demands of architectural expressiveness. The free-form structure is beautiful and has a strong visual impact effect. Can produce a variety of flexible geometric shapes to meet the requirements of architectural design. It is the main problem that needs to be solved at present. In view of many complex interior and outer building boundary conditions that may exist in practical engineering, this paper applies B-spline curve theory and Delaunay triangulation technology to triangulate the plane design domain. The initial model of free-form surface with complex design domain is established by projecting onto B-spline surface. In this paper, a new method of free-form structure is proposed, which uses a few key points to adjust the shape of surface. The main contents are as follows: 1. The establishment of the initial model of free-form surface structure is the foundation of free-form structure formation. Based on the theory of B-spline curve, this paper makes use of the odd periodic parameterized B-spline curve to generate a variety of times and many curves together to form the outer and inner boundary of the building, which fully satisfies the rich boundary modeling in architectural design. The requirement of internal reservation of holes is more practical in engineering practice 2.To determine the evaluation objective function in the process of optimization, it is necessary to evaluate the optimization results obtained from each step. The contents of the evaluation need to take into account the overall stress of the structure, the relationship between the objective function of the evaluation and the variables should be realized by program, and the expression should be as simple as possible. In this paper, strain energy is used as the evaluation index. Strain energy can synthesize the overall mechanical properties of the reaction structure, and the structure with reasonable mechanical properties can be found by the single objective optimization of the strain energy. To ensure the increase of the overall stiffness of the structure, and finally transfer the load by the internal force of the membrane. 3. In order to obtain the reasonable structure shape, it is necessary to combine the geometric creating method of the free form surface with the structural shape optimization algorithm. By optimizing and adjusting the shape of the surface to determine the parameters, the free-form surface with beautiful shape and reasonable force is gradually obtained. In this paper, the expression of strain energy sensitivity of the key points on the B-spline surface is derived in detail, and the step size is given. The vertical coordinates of the key points on the surface are adjusted in the direction of negative sensitivity gradient so that the final structural strain can reach a lower level and the sensitivity tends to zero. The surface of the free-form surface is smooth and continuous, no secondary machining is required, and the sensitivity of strain energy of the key points on the surface is only calculated. At the same time, the surface boundary is diverse, and the concave and convex surface is rich. This method is not only a more in-depth theoretical study, but also has high engineering practicability.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU318

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