發(fā)布時間：2019-01-05 03:34

【摘要】：隨著物質(zhì)條件的不斷豐富和生活水平的不斷提高,人們對建筑的要求不再僅僅停留在安全、經(jīng)濟(jì)和實用層面,人們開始更多的關(guān)注建筑的美學(xué)價值。樹狀結(jié)構(gòu)作為仿生建筑的一種,其造型優(yōu)美,與自然協(xié)調(diào)統(tǒng)一,受力高效合理,能用較小的桿件支撐起較大的空間,在現(xiàn)代建筑領(lǐng)域有著廣闊的應(yīng)用前景。本文所建立的空間樹狀結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)方法是一種綜合了幾何理論和數(shù)值分析的高效研究方法。幾何理論的應(yīng)用是指利用分形理論和B樣條曲線理論進(jìn)行初始樹狀結(jié)構(gòu)的幾何創(chuàng)建過程。本文綜合考慮樹狀結(jié)構(gòu)的自相似性和力的傳遞特性,應(yīng)用分形理論創(chuàng)構(gòu)出更貼近自然、符合審美的下部樹狀支撐,并通過編程實現(xiàn)對初始樹狀結(jié)構(gòu)拓?fù)涞牟倏亍Ｍ瑫r,本文考慮到實際工程中可能存在的復(fù)雜內(nèi)外邊界條件,利用拓展的參數(shù)化(2m-1)次周期B樣條曲線函數(shù),生成多種次數(shù)、多條曲線共同圍成的閉合光滑平面邊界,使上部荷載面造型豐富、靈活多變。然后,根據(jù)內(nèi)外邊界條件和樹狀支撐末級分枝的端點位置,利用Delaunay三角剖分原理對上部荷載面進(jìn)行網(wǎng)格劃分,以方便對整體結(jié)構(gòu)進(jìn)行有限元計算和分析。其次,對已有的初始樹狀結(jié)構(gòu)進(jìn)行數(shù)值分析,提出了空間樹狀結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)問題的數(shù)學(xué)模型。節(jié)點位置和單元布置分別決定了結(jié)構(gòu)的形狀和拓?fù)?而結(jié)構(gòu)的形狀和拓?fù)溆譀Q定了結(jié)構(gòu)的力學(xué)性能。故本文樹狀結(jié)構(gòu)優(yōu)化模型是以節(jié)點位置和單元拓?fù)錇樽宰兞?通過節(jié)點移動和單元增減,最終實現(xiàn)應(yīng)變能最小的目標(biāo)函數(shù),得到受力高效合理的樹狀結(jié)構(gòu)。其中,節(jié)點移動又分為下部自由節(jié)點移動和上部約束節(jié)點移動兩方面。在此基礎(chǔ)上,通過截面優(yōu)化達(dá)到材料高效利用的目的,使該方法更具工程經(jīng)濟(jì)性。初始結(jié)構(gòu)的幾何創(chuàng)建是結(jié)構(gòu)形態(tài)創(chuàng)構(gòu)的第一步,初始模型的合理與否對進(jìn)化過程和最終形態(tài)有著深遠(yuǎn)影響,是尋求“良好建筑結(jié)構(gòu)形態(tài)”的關(guān)鍵步驟。本文提出的初始樹狀結(jié)構(gòu)的幾何創(chuàng)建方法操作簡單,便于根據(jù)建筑條件進(jìn)行修改,生成的建筑邊界靈活多變,樹狀支撐造型美觀,傳力高效合理。應(yīng)變能是結(jié)構(gòu)的狀態(tài)量,它是指結(jié)構(gòu)在外力作用下以應(yīng)力和應(yīng)變的形式儲存在結(jié)構(gòu)內(nèi)部的勢能。在相同的靜力荷載作用下,結(jié)構(gòu)剛度越大,所產(chǎn)生位移越小,結(jié)構(gòu)應(yīng)變能也越小,此時結(jié)構(gòu)內(nèi)力主要以軸力為主,因此應(yīng)變能這一標(biāo)量能很好的體現(xiàn)出結(jié)構(gòu)的整體剛度和荷載傳遞效率。本文通過多個算例論述了以應(yīng)變能為目標(biāo)函數(shù)的合理性,并對各個算例進(jìn)行分析得到空間樹狀結(jié)構(gòu)的形態(tài)特征和力學(xué)特征,為樹狀結(jié)構(gòu)的設(shè)計及工程應(yīng)用提供依據(jù)。
[Abstract]:With the constant enrichment of material conditions and the improvement of living standards, people's demands on architecture are no longer confined to the level of safety, economy and practice, and people begin to pay more attention to the aesthetic value of architecture. As a kind of bionic architecture, tree structure has beautiful shape, harmony with nature, high efficiency and reasonable force, and can support large space with smaller members. It has a broad application prospect in the field of modern architecture. In this paper, the spatial tree structure is an efficient method which combines geometric theory and numerical analysis. The application of geometric theory refers to the geometric creation process of initial tree structure using fractal theory and B-spline curve theory. In this paper, considering the self-similarity of tree structure and the transfer characteristic of force, the author applies fractal theory to construct the lower tree support, which is closer to nature and aesthetic, and controls the topology of initial tree structure by programming. At the same time, taking into account the complex internal and external boundary conditions that may exist in practical engineering, using the extended parameterized (2m-1) subperiodic B-spline curve function, a closed smooth plane boundary is generated, which is surrounded by multiple times and multiple curves. The upper load surface is rich in shape and flexible. Then, according to the internal and external boundary conditions and the end point position of the last branch of tree bracing, the upper load surface is meshed by using the Delaunay triangulation principle, so as to facilitate the finite element calculation and analysis of the whole structure. Secondly, the existing initial tree structure is numerically analyzed, and the mathematical model of spatial tree structure is proposed. The position of nodes and the layout of elements determine the shape and topology of the structure, and the shape and topology of the structure determine the mechanical properties of the structure. Therefore, the tree structure optimization model in this paper takes node position and unit topology as independent variables, through node movement and element increase and subtraction, the objective function of minimum strain energy is finally realized, and a tree structure with high efficiency and reasonable force is obtained. Among them, node movement is divided into two aspects: lower free node movement and upper constrained node movement. On the basis of this, the material can be used efficiently by cross-section optimization, which makes the method more economical. The geometric creation of initial structure is the first step of structural form creation. Whether the initial model is reasonable or not has a profound influence on the evolution process and the final form. It is the key step to seek "good architectural structure form". The geometric creation method of the initial tree structure presented in this paper is simple to operate and easy to modify according to the building conditions. The generated building boundary is flexible and changeable, the tree shape is beautiful, and the transfer of force is efficient and reasonable. Strain energy is the state quantity of structure. It refers to the potential energy of structure stored in the form of stress and strain under the action of external force. Under the same static load, the greater the stiffness of the structure, the smaller the displacement and the smaller the strain energy of the structure. At this time, the main internal force of the structure is axial force. Therefore, the strain energy as a scalar can well reflect the overall stiffness of the structure and load transfer efficiency. In this paper, the rationality of taking strain energy as the objective function is discussed through several examples, and the morphological and mechanical characteristics of the spatial tree structure are obtained through the analysis of each example, which provides the basis for the design and engineering application of the tree structure.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TU318

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本文編號：2401209