基于分形理论的仿生树状结构研究

发布时间：2018-05-02 18:03

本文选题：树状结构 + 分形理论　；参考：《哈尔滨工业大学》2014年硕士论文

【摘要】：仿生树状结构以其受力合理，形态优美的特点被广泛应用于空间建筑结构中。近年来越来越多的仿生树状结构应用于实际工程，因此对于仿生树状结构形态创构方法的研究具有很高的理论和应用价值。本文所论述的仿生树状结构形态创构方法目的是为建筑设计提供方案，以结构优化理论为手段，在尽可能提高结构受力性能的前提下给出形状优美的结构形式。结构优化理论及分形理论的应用为本方法的核心内容，其中包括形状优化，，拓扑变化以及截面优化。本文主要介绍了分形理论在本方法中应用的可能性，以应变能为目标函数的优化模型的合理性，同时介绍了节点应变能敏感度与单元敏感度的数学意义及力学意义。本方法针对不同的建筑意图以及约束条件，论述了固定初始拓扑形式和变化拓扑形式两种不同的结构形态创构策略，并分别通过例题论述了本方法的合理性以及所得到结构的形态特征。固定初始拓扑形式是在结构初期给定结构拓扑关系，在优化过程中根据节点应变能敏感度对结构形状进行调整，当应变能下降到某一收敛值时停止优化，最后对杆件截面进行调整得到最终结构，这种方法适用于建筑外观要求较为严格，对于建筑拓扑形状有特定要求的情况。可变拓扑的形态创构方法是给定简单初始拓扑结构，应用节点应变能敏感度理论对结构形状进行调整，应变能收敛后应用单元应变能敏感度理论结合分形理论对指定杆件进行分形生长，从而改变结构拓扑，最后对杆件截面进行优化得到最终结构。该方法适用于建筑外观要求较为宽松，对结构拓扑形状没有特定要求的情况，所得到的结构从结构形式上来讲更加自由，新拓扑的生成使结构出现了新的传力路径，造成了应变能的突变，使得应变能可以在形状优化后继续降低，所得到的结构在力学层面更加合理。本文所论述的仿生树状结构形态创构方法将结构在静荷载下应变能作为目标函数，考察结构进化过程中应变能，平均弯矩，最大弯矩，平均轴力及最大竖向位移等特征量，得出仿生树状结构的受力特征，为仿生树状结构的设计及工程应用做参考。
[Abstract]:The bionic tree structure is widely used in spatial architecture because of its reasonable force and graceful shape. In recent years, more and more bionic tree structures have been applied to practical engineering. Therefore, it is of great theoretical and application value for the study of the bionic tree structure formation method.
The aim of this paper is to provide a scheme for architectural design. With structural optimization theory as a means, a graceful form is given on the premise of improving the strength of the structure as far as possible. The core content of this method is the application of structure optimization theory and fractal theory, including shape optimization. This paper mainly introduces the possibility of the application of the fractal theory in this method, the rationality of the optimization model with the strain energy as the objective function, and the mathematical meaning and the mechanical significance of the strain energy sensitivity of the node and the unit sensitivity.
In view of different architectural intentions and constraints, this paper discusses two different structural forms of structural formation strategy with fixed initial topology and change topology, and the rationality of this method and the morphological characteristics of the structure are discussed respectively through examples. The fixed initial topology is a given structure topology at the initial stage of the structure. In the process of optimization, the structure shape is adjusted according to the strain energy sensitivity of the node. When the strain energy is reduced to a certain convergent value, the optimization is stopped. Finally, the final structure is adjusted to the cross section of the rod. This method is suitable for the strict requirements of the architectural appearance and the specific requirements for the topology shape of the building. The formation method of the flutter is a given simple initial topology, and the structure shape is adjusted by the strain energy sensitivity theory of the node. After the strain energy convergence is convergent, the element strain energy sensitivity theory is applied to the specified rod to grow fractal, thus the structural extension is changed. Finally, the optimization of the cross section of the rod is finally obtained. Structure. This method is suitable for more relaxed architectural appearance requirements and no specific requirements for the structure topology. The structure obtained is more free from the structure form. The generation of the new topology makes the structure appear a new force path, cause the mutation of strain energy, so that the strain energy can continue to be reduced after the shape optimization. The obtained structure is more reasonable at the mechanical level.
In this paper, the bionic tree structure form method is used to study the strain energy, the average bending moment, the maximum bending moment, the average axial force and the maximum vertical displacement in the process of structural evolution, and the stress characteristics of the bionic tree structure, which are the design and engineering of the bionic tree structure. For reference.

【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】：TU399

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