發(fā)布時間：2018-05-02 18:03

  本文選題：樹狀結(jié)構(gòu) + 分形理論��； 參考：《哈爾濱工業(yè)大學》2014年碩士論文

【摘要】：仿生樹狀結(jié)構(gòu)以其受力合理，形態(tài)優(yōu)美的特點被廣泛應(yīng)用于空間建筑結(jié)構(gòu)中。近年來越來越多的仿生樹狀結(jié)構(gòu)應(yīng)用于實際工程，因此對于仿生樹狀結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)方法的研究具有很高的理論和應(yīng)用價值。 本文所論述的仿生樹狀結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)方法目的是為建筑設(shè)計提供方案，以結(jié)構(gòu)優(yōu)化理論為手段，在盡可能提高結(jié)構(gòu)受力性能的前提下給出形狀優(yōu)美的結(jié)構(gòu)形式。結(jié)構(gòu)優(yōu)化理論及分形理論的應(yīng)用為本方法的核心內(nèi)容，其中包括形狀優(yōu)化，，拓撲變化以及截面優(yōu)化。本文主要介紹了分形理論在本方法中應(yīng)用的可能性，以應(yīng)變能為目標函數(shù)的優(yōu)化模型的合理性，同時介紹了節(jié)點應(yīng)變能敏感度與單元敏感度的數(shù)學意義及力學意義。 本方法針對不同的建筑意圖以及約束條件，論述了固定初始拓撲形式和變化拓撲形式兩種不同的結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)策略，并分別通過例題論述了本方法的合理性以及所得到結(jié)構(gòu)的形態(tài)特征。固定初始拓撲形式是在結(jié)構(gòu)初期給定結(jié)構(gòu)拓撲關(guān)系，在優(yōu)化過程中根據(jù)節(jié)點應(yīng)變能敏感度對結(jié)構(gòu)形狀進行調(diào)整，當應(yīng)變能下降到某一收斂值時停止優(yōu)化，最后對桿件截面進行調(diào)整得到最終結(jié)構(gòu)，這種方法適用于建筑外觀要求較為嚴格，對于建筑拓撲形狀有特定要求的情況�？勺兺負涞男螒B(tài)創(chuàng)構(gòu)方法是給定簡單初始拓撲結(jié)構(gòu)，應(yīng)用節(jié)點應(yīng)變能敏感度理論對結(jié)構(gòu)形狀進行調(diào)整，應(yīng)變能收斂后應(yīng)用單元應(yīng)變能敏感度理論結(jié)合分形理論對指定桿件進行分形生長，從而改變結(jié)構(gòu)拓撲，最后對桿件截面進行優(yōu)化得到最終結(jié)構(gòu)。該方法適用于建筑外觀要求較為寬松，對結(jié)構(gòu)拓撲形狀沒有特定要求的情況，所得到的結(jié)構(gòu)從結(jié)構(gòu)形式上來講更加自由，新拓撲的生成使結(jié)構(gòu)出現(xiàn)了新的傳力路徑，造成了應(yīng)變能的突變，使得應(yīng)變能可以在形狀優(yōu)化后繼續(xù)降低，所得到的結(jié)構(gòu)在力學層面更加合理。 本文所論述的仿生樹狀結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)方法將結(jié)構(gòu)在靜荷載下應(yīng)變能作為目標函數(shù)，考察結(jié)構(gòu)進化過程中應(yīng)變能，平均彎矩，最大彎矩，平均軸力及最大豎向位移等特征量，得出仿生樹狀結(jié)構(gòu)的受力特征，為仿生樹狀結(jié)構(gòu)的設(shè)計及工程應(yīng)用做參考。
[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.

【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TU399

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