土建畢業(yè)設計外文翻譯--基于結構約束探索不規(guī)則網(wǎng)狀鋼和玻璃外殼形式

1、<p>　　基于結構約束探索不規(guī)則網(wǎng)狀鋼和玻璃外殼形式</p><p>　　Sigrid Adriaenssens, M.ASCE1; Laurent Ney2; Eric Bodarwe3; and Chris Williams4</p><p>　　摘要:在對荷蘭阿姆斯特丹荷蘭海事博物館頂部覆蓋的一種高效的結構形式進行探究的文章中，作者簡要討論了作用力對最早的玻璃屋頂覆蓋物的

2、影響。在20世紀末到21世紀初，外露的鋼骨架玻璃殼設計慢慢出現(xiàn)。這些設計形式在從雕塑到幾何再向結構轉變。通過荷蘭海事博物館鋼玻璃殼屋頂?shù)陌l(fā)展，對它的挑戰(zhàn)性設計的討論得出了設計者在基于一個詩意的幾何思想的基礎上，對尋求有效的結構鏈形式的探索。本文提出了一種建筑結構設計方法。這種方法稍微適和用數(shù)值模擬方法探索目的是在所有的的三角化、四面性和五面性的網(wǎng)面中實現(xiàn)平面化的結構鏈模形。然而，如何通過分析玻璃面的途徑將其很好的解決并呈現(xiàn)給人們?yōu)閷崿F(xiàn)平

3、面化向人們提出了挑戰(zhàn)。對照此種方法得到麥克斯韋互惠網(wǎng)絡圖。最后，雕琢出的平面向人們展示了典雅、耐用。</p><p>　　DOI:10.1061 /(土木)ae.1943 - 5568.0000074。©2012美國土木工程師學會。</p><p>　　CE數(shù)據(jù)庫主題詞:設計;鋼材;玻璃;古跡;屋頂;荷蘭。</p><p>　　關鍵詞:形狀;概念設計;模型

4、探究;鋼玻璃殼體結構;歷史意義的庭院;平面化感官;結構約束;麥克斯韋互惠網(wǎng)絡。</p><p>　　正文：隨著工業(yè)革命的興起,玻璃金屬結構出現(xiàn)受兩個因素支配: 其一、在人口過多的城市, 社會對綠色和安靜的空間的渴望；其二、新的建筑材料(玻璃和鐵) 的出現(xiàn)。</p><p>　　在十八世紀初,第一溫室裝以玻璃的屋頂出現(xiàn)在人們生活的中。它們的高昂的建設和維護成本(由于玻璃和必需的供暖系統(tǒng))讓它

5、們成為精英階層的標志。他們的彎曲形狀 [(1) 嵴溝連跨型 例如, 查特斯沃思莊園, 英國(建于1834年), 與(2) 拱形, 例如, 裘園（倫敦市郊著名植物園）, 英國 (建于1844年) (Kohlmaier and Von Sartory 1991)]允許稀疏的陽光進入室內并照在柑橘和檸檬樹上(因此,名稱橘園)。其他品種的溫室植物、灌木和奇異的植物也被安置在橘園。其中棕櫚樹, 扮演著大量的宗教色彩,是尤其令人印象深刻的和有名的植

6、物,從而也把溫室的形象進一步提升。</p><p>　　十九世紀中期，溫室類型學已全面發(fā)展，由此便產(chǎn)生了文化室、暖房以及冬景花園[例如, 皇家溫室、拉肯,比利時(建于1876年)現(xiàn)于Fig. 1 (Woods and Swartz 1988)].冬季花園是本文特別感興趣的,因為它是一個社交場合，與一棟私人豪宅或公共建筑及其接近。在十九世紀下半葉，大規(guī)模生產(chǎn)的負擔得起的鐵進一步鼓勵了高層和大跨度由鋼材和玻璃建成的展

7、廳的設計和施工。大量光線進入展覽區(qū)的建筑物，如水晶宮、英國(建于1851年)(如圖所示在Fig. 1)。其如網(wǎng)狀的鋼結構骨架是預制的，后來被拆除,從海德公園搬運至倫敦南部的西登哈姆。不幸的是,它在1936年毀于火災。</p><p>　　19世紀后半期和20世紀早期，公共建筑物屋頂?shù)脑O計和施工又經(jīng)歷了一個很大的提升，冬景花園不再種植植物，而是覆蓋在重要的歷史公共建筑的庭院上方[例如 , 大英博物館的大院子, Un

8、ited Kingdom, 英國; 見 Fig. 1; the Deutschen Historischen Museum, and Museum fur Hamburgische Geschichte, 德國(如期分別在2001和2004年建成的Schlaich Bergermann and Partners); 和the Smithsonian Institute,Washington, DC (Foster and Partner

9、s, and Buro Happold in 2001)]。頂部覆蓋玻璃的單層鋼骨架的形狀由雕塑、幾何、物理以及施工條件等因素共同決定。最近這些結構的重新崛起，伴隨著由數(shù)字化設計演化出的工具，使得設計師能夠開發(fā)和分析出更多大膽和自由的幾何設計。</p><p><b>　　單層玻璃鋼骨架結構</b></p><p>　　今天的設計師（有過設計和工程背景）在設計這些非種

10、植植物的冬季花園時主要遵循以下四個因素: 實施現(xiàn)狀,建筑美學,建筑幾何形狀和建筑物結構效率等。</p><p><b>　　現(xiàn)代冬季花園</b></p><p>　　在過去的二十年里, 存在著這樣與歷史有關的公共建筑，它們已經(jīng)能夠通過擴展建筑物的中部空間適應室內或室外氣候。那些狹小的建筑物通常利用中部空間提供光亮。鋼結構玻璃外殼為設計的挑戰(zhàn)提供了唯一的解決方案。歷史的

11、顯示，設計師在研發(fā)設計殼體結構的過程中往往會受到一系列約束條件的限制。其限制條件通常包括高度的限制以及強加于現(xiàn)有建筑物,尤其是水平方向，最大負荷的限制。大英博物館法院屋頂是滑動軸承支撐,這樣就沒有水平推力落在歷史博物館的砌體墻上(威廉姆斯2001)。回顧最近的設計我們就會意識到，推動鋼結構玻璃殼結構設計的因素主要是建筑形態(tài)美學而非結構的性能。</p><p><b>　　建筑美學</b>&l

12、t;/p><p>　　利用可用幾何數(shù)字建模工具，更多的建筑師通過把他們的工作建立在審美(通常是主觀的)條件上來實現(xiàn)結構的布景效果。它們的結構設計主要取決于結構形式的創(chuàng)新,而非結構的重力荷載條件。因此，這種特殊的設計方法可以解決結構缺乏結構效率的問題。不幸的是, 這種結構解決方案通常必須使用一些笨拙的、重要的材料來構造這些建筑形態(tài)。這些自由延伸的構造會在建筑物產(chǎn)生不利的內力，也會在建筑物的表面造成無法預料的其它不利力的

13、影響。這些形狀依靠彎曲支撐受力-最有效的基本負荷的方法。然而，設計師往往忽略這樣一個事實,即建筑物自由的結構形式由傳統(tǒng)的建筑和結構方式構造產(chǎn)生。弗蘭克蓋里,普利茲克獎建筑師, 促進了這種建筑設計進程, 他傳達過這種建筑設計的想法而沒有過這種建筑設計(Shelden2002)。一個合理化的設計，在初步設計階段，需要超越傳統(tǒng)布局經(jīng)驗而且要以結構的完整性設計為中心(Leach et al . 2004)。</p><p&g

14、t;　　形成一個初步的建筑結構形態(tài)需要一個強大的工程師和承包商團隊。例如, Nuovo Polo Fiera Milano, 意大利 (建于2004年) (Guillaume et al. 2005) 的屋頂殼體設計概念是由建筑師馬希米亞諾·?？怂_斯,然后交給結構工程師和承包商Mero TSK 集團解決結構上和構造上的關系后確定的(見圖 2) (Basso et al. 2009)。</p><p>&

15、lt;b>　　幾何造型</b></p><p>　　幾何學是一種工具, 古代建筑模型的構造就已經(jīng)使用。當然，這也一直受到立體解析幾何和設計者想象力強加的規(guī)則的限制。幾個世紀以來,建筑學已經(jīng)能夠圍繞簡單的幾何圖形來判斷建筑物在結構和構造上的質量。 [我們可以從花之圣母大教堂的圓頂及其最近的混凝土外殼的設計中找到這樣的例子?；ㄖツ复蠼烫玫膱A頂，意大利(建于1436年),由菲利普·布魯內萊

16、斯基；其最近的混凝土外殼，費利克斯·坎德拉(Moreyra Garlock and Billington 2008)] 旋轉彎曲型屋面,移動型屋面,和大小可變型屋面能讓它們更好的組合成殼體屋面結構，并分散成一個個小小的單元。在這種背景下, 耶爾格·施萊希和漢斯·舍貝爾在鋼殼結構的工作是一種創(chuàng)新。他們設計了將屋面分為平面四邊形網(wǎng)格方法，能夠獲得正確的移動型屋面,和大小可變型屋面。柏林動物園的HippoHous

17、e，德國（建于1996年），由建筑師設計Grieble和Schlaich Bergermann以及合作伙伴(Schober 2002,Glymph et al . 2004)利用這種方法設計的一個優(yōu)美的鋼殼,見圖3。</p><p>　　通過結構形式考慮結構效率</p><p>　　幾乎所有傳統(tǒng)的結構設計原理(從材料選取、剖面圖,節(jié)點類型, 整體微分幾何、和支撐條件), 整體微分幾何學都是

18、確定一個殼體結構是否是穩(wěn)定的,安全的,足夠的支撐。每個擁有精美結構網(wǎng)絡的大跨度殼體結構都是由大量細小模塊組成。第一個此類結構的設計在于設置精確的邊界條件,在這個精確的邊界內外殼的形狀可以向外拓展。在實現(xiàn)膜強度的穩(wěn)定性，曲線形狀是至關重要的。彎曲的殼體需要通過尋找“正確”的幾何形狀來避免因自重而只有膜起作用的結果。薄膜效應使材料的性能得以充分發(fā)揮。結構設計最重要的的挑戰(zhàn)首先在于確定約束骨架的殼體的三維(3 d)表面。在二十世紀,建筑師和工

19、程師[高迪(Huerta 2003),奧托(Otto et al .1995), 易思樂(Billington 2008)]嘗試利用物理形式尋找這樣一種方法,在對于一個給定的材料,建立一組邊界條件和重力荷載,以尋找有效的三維結構形狀。為鋼殼結構找到一個纜索系統(tǒng)的重要性首先在于這樣一個事實，自重(鋼和玻璃引起的重力負載) 主要貢獻的負載被抵消。子模塊需要軸向加載使截面輪廓最有效地受力。利用數(shù)值模擬形式尋找方法[力密度法(Schek 197

20、4)和動態(tài)松</p><p>　　在NSA庭院競爭設計鋼玻璃殼體結構</p><p>　　在不久的將來，荷蘭海事博物館計劃徹底的改造項目。十七世紀歷史建筑成為受限空間阻礙了游客的運行。博物館的院子需要集成到旅客流通空間,且要規(guī)避天氣影響,保持最小的室內溫度。這樣，一個邀請設計大賽被舉辦，為這座歷史建筑增加更多附加價值一個新的玻璃屋頂產(chǎn)生了。2005年,奈伊和其合作伙伴,一個總部位于布魯塞爾

21、的工程設計咨詢公司, 鋼和玻璃結構外殼設計贏得了這次比賽。外殼的制造和施工在2009年和2011年之間。2012年,該項目被授予阿姆斯特丹建筑獎。</p><p>　　Finding the Form of an Irregular Meshed Steel and Glass Shell</p><p>　　Based on Construction Constraints</p&

22、gt;<p>　　Sigrid Adriaenssens, M.ASCE1; Laurent Ney2; Eric Bodarwe3; and Chris Williams4</p><p>　　Abstract: In the context of the search for an efficient structural shape to cover the Dutch Maritime Mu

23、seum courtyard in Amsterdam, Netherlands,</p><p>　　the authors briefly discuss the driving design factors that influenced the earliest glass roof coverings. The trends that emerged during the</p><

24、p>　　late 20th and early 21st century in the design of skeletal steel glass shells are exposed. These design developments range from sculptural to</p><p>　　geometric and structural intentions. The discussi

25、on of the competition design development of the Dutch Maritime Museum steel glass shell</p><p>　　roof shows the quest for a structurally efficient catenary form based on a poetic geometric idea. This paper p

26、resents a construction-driven design</p><p>　　methodology that slightly adapts the numerical form found catenary shape with the objective of achieving planarity in all the triangulated, foursided</p>

27、<p>　　and five-sided mesh faces. The challenge of facet planarity is gracefully solved by an analytical origami approach and presented. This</p><p>　　approach is compared with finding the Maxwell recipr

28、ocal network diagram. The final faceted shape shows elegance and structural efficiency.</p><p>　　DOI: 10.1061/(ASCE)AE.1943-5568.0000074. © 2012 American Society of Civil Engineers.</p><p>

29、　　CE Database subject headings: Design; Steel; Glass; Historic sites; Roofs; Netherlands.</p><p>　　Author keywords: Shape; Conceptual design; Form finding; Steel glass shell; Historic courtyard; Planarity fa

30、ces; Construction constraint;</p><p>　　Maxwell reciprocal network.</p><p>　　Introduction</p><p>　　In the wake of the Industrial Revolution, glass metal structures</p><p&g

31、t;　　appeared as a result of two factors: society’s desire for green, quiet</p><p>　　spaces in overpopulated cities, and the scientific emergence of new</p><p>　　construction materials (glass and

32、 iron).</p><p>　　In the early nineteenth century, the first greenhouses with a</p><p>　　glazed roof appeared as living spaces. Their tall construction and</p><p>　　maintenance costs

33、 (because of the glass and the required heating</p><p>　　system) made them style icons of the elite. Their curved shapes</p><p>　　[(1) ridge and furrow e.g., Chatsworth, United Kingdom (built<

34、;/p><p>　　in 1834), and (2) vaulted, e.g., Kew, United Kingdom (built in</p><p>　　1844) (Kohlmaier and Von Sartory 1991)] allowed the sparse</p><p>　　sunlight into the space and hit th

35、e citrus and lime trees (hence, the</p><p>　　name orangery). Other varieties of tender plants, shrubs, and</p><p>　　exotic plants were also housed in the orangery. The introduction</p>&l

36、t;p>　　of the palm tree, an impressive and prestigious plant with large</p><p>　　religious significance, pushed the shape of the greenhouse further</p><p><b>　　upwards.</b></p&g

37、t;<p>　　In the middle of the nineteenth century, the development of</p><p>　　greenhouse typologies was in full swing, and resulted in culture</p><p>　　houses, conservatories, and winter g

38、ardens [e.g., the Royal greenhouses,</p><p>　　Laeken, Belgium (built in 1876) shown in Fig. 1 (Woods and</p><p>　　Swartz 1988)]. The winter garden is of particular interest to this</p>&l

39、t;p>　　paper because it defines a social meeting place adjacent to a private</p><p>　　mansion or public building.</p><p>　　Mass production of affordable iron in the second half of the</p>

40、;<p>　　nineteenth century further encouraged the design and construction</p><p>　　of tall and large span exhibition halls made of cast and wrought iron</p><p>　　and glass. Plenty of light

41、 entered the exhibition areas of buildings,</p><p>　　such as the Crystal Palace, United Kingdom (built in 1851) (shown</p><p>　　in Fig. 1). Its filigree iron structural skeleton was prefabricate

42、d, and</p><p>　　it was subsequently dismantled and moved from Hyde Park to</p><p>　　Sydenham in South London. Unfortunately, it was destroyed by fire</p><p><b>　　in 1936.</

43、b></p><p>　　The second half of the 20th and the early 21st centuries experienced</p><p>　　a new uprising of the design and construction of roofs over</p><p>　　social gathering pl

44、aces, winter gardens without plants, covering</p><p>　　courtyards of historically important public buildings [e.g., the great</p><p>　　courtyard of the British Museum, United Kingdom; see Fig. 1

45、; the</p><p>　　Deutschen Historischen Museum, and Museum fur Hamburgische</p><p>　　Geschichte, Germany (both Schlaich Bergermann and Partners, built</p><p>　　in 2001 and 2004, respe

46、ctively); and the Smithsonian Institute,</p><p>　　Washington, DC (Foster and Partners, and Buro Happold in 2001)].</p><p>　　The shapes of these glass-covered, single-layered steel skeletal</p

47、><p>　　shells were driven by a combination of sculptural, geometric,</p><p>　　physical, and constructional considerations (Williams 2000). The</p><p>　　recent re-emergence of these str

48、uctures goes hand in hand with the</p><p>　　evolution of digital design tools that enable the designer to develop</p><p>　　and analyze more free and daring geometries.</p><p>　　Sing

49、le-LayeredSteelSkeletalShellsCoveredwithGlass</p><p>　　Today’s designers (either from an architectural or engineering</p><p>　　background) of these nonbotanical winter garden shells seem to</

50、p><p>　　be guided by one or more of the following four driving factors: </p><p>　　Fig. 1. (a) Laeken winter garden (Belgium, built in 1875) still serves as</p><p>　　a social meeting pl

51、ace. (Jackson 2007; reprinted with permission from</p><p>　　the photographer); (b) prefabricated Crystal Palace (United Kingdom,</p><p>　　built in 1851) was dismantled soon after its intended us

52、e (reprinted</p><p>　　from http://commons.wikimedia.org/wiki/File:Crystal_Palace.PNG,</p><p>　　originally from Tallis’ History and Criticism of the Crystal Palace.</p><p>　　1852); (

53、c) British Museum Courtyard (United Kingdom, built in 2000)</p><p>　　steel roof adds value to the museum by expanding the useable circulation</p><p>　　space (image by authors)</p><p&g

54、t;　　imposed existing situation, sculptural architectural esthetics,</p><p>　　geometric shape, and structural efficiency through form.</p><p>　　Imposition on an Existing Situation: The Modern<

55、/p><p>　　Winter Garden</p><p>　　In the last two decades, existing historically relevant public</p><p>　　buildings with a central open courtyard have been adapted to extend</p>&

56、lt;p>　　the useable floor area to an indoor/outdoor climate. These</p><p>　　generally narrow buildings count on the courtyard for daylight.</p><p>　　Steel and glass shells offer a unique solut

57、ion to this design challenge.</p><p>　　The historic context for these shells imposes a series of</p><p>　　design constraints within which the designer has the freedom to</p><p>　　de

58、velop the shell’s form. The boundary conditions often include</p><p>　　height restrictions and limits upon the maximumextra load that can</p><p>　　be imposed on the existing building, particular

59、ly in a horizontaldirection. The British Museum Court Roof is supported on sliding</p><p>　　bearings so that no horizontal thrust is exerted on the historic</p><p>　　masonry walls of the museum

60、(Williams 2001). In the reviewing</p><p>　　the design of recently realized steel shells, the driving design factor</p><p>　　more often seems to be architectural scenographic esthetics rather<

61、/p><p>　　than structural performance.</p><p>　　Sculptural Architectural Esthetics</p><p>　　With the available geometric digital modeling tools, more architects</p><p>　　ba

62、se their work on esthetic (and often subjective) considerations to</p><p>　　achieve scenographic effects. This sculptural design intent can be</p><p>　　appreciated for its inventiveness of plast

63、ic forms, but not for its</p><p>　　consideration of gravity loads. This particular design approach thus</p><p>　　raises questions from a structural point of view with respect to the</p>&

64、lt;p>　　resulting lack of structural efficiency. Unfortunately, the structural</p><p>　　solutions necessary to make these sculptural shapes possible typically</p><p>　　use an awkward and signi

65、ficant accumulation of material.</p><p>　　These free-form shapes often lead to unfavorable internal forces and</p><p>　　under loading do not allow membrane stresses to develop within the</p&g

66、t;<p>　　surface. These shapes then rely on bending action—the least effective</p><p>　　of all basic load carrying methods. Designers often ignore the</p><p>　　fact that the free form is m

67、ade up of conventional constructional and</p><p>　　structural means. Frank Gehry, the Pritzker prize-winning architect,</p><p>　　promotes this architectural process, which expresses sculptural&l

68、t;/p><p>　　intentions but is disconnected from any sculptural intent (Shelden</p><p>　　2002). A rationalization is needed at the preliminary design stage</p><p>　　that goes beyond this

69、 scenographic experience and concentrates on</p><p>　　the structural integrity of the design (Leach et al. 2004).</p><p>　　The evolution of an initial sculptural shape into a constructable</p

70、><p>　　structure needs a strong team of engineers and contractors. For example,</p><p>　　the conceptual design for the shell of the Nuovo Polo Fiera</p><p>　　Milano, Italy (built in 20

71、04) (Guillaume et al. 2005) was developed</p><p>　　by the architect Massimiliano Fuksas and then handed over to the</p><p>　　engineers Schlaich Bergermann and Partners and contractor Mero</p&

72、gt;<p>　　TSK Group for the development of the structural and constructional</p><p>　　rationale for the project (see Fig. 2) (Basso et al. 2009).</p><p>　　Geometric Shape</p><p&

73、gt;　　Geometry is a tool that has been used since antiquity for the development</p><p>　　of architectural shapes. These forms are thus limited by</p><p>　　the rules imposed by analytical geometry

74、 and the designer’s imagination.</p><p>　　Through the centuries, architecture has developed around</p><p>　　“simple” geometries chosen for their constructive or structural</p><p>　　

75、qualities. [Examples can be found in the design of the cupola of</p><p>　　the cathedral Santa Maria del Fiore, Italy (built in 1436), by Filippo</p><p>　　Brunelleschi and more recently the thin

76、concrete shells by Felix</p><p>　　Candela (Moreyra Garlock and Billington 2008).] Surfaces of revolution,</p><p>　　translational surfaces, and scale-trans surfaces lend themselves</p><

77、;p>　　excellently to shell action and discretization into subelements.</p><p>　　In this context, the work of Jorg Schlaich and Hans Schober on steel</p><p>　　shells is innovative. They devised

78、 a method to find the right translational</p><p>　　or scale-trans surface that can be divided into four-sided</p><p>　　planar meshes. The HippoHouse of the Berlin Zoo, Germany (built</p>

79、<p>　　in 1996), designed by architect Grieble and Schlaich Bergermann</p><p>　　and Partners (Schober 2002, Glymph et al. 2004) exploits this approach</p><p>　　in an elegant steel shell, as

80、shown in Fig. 3.</p><p>　　Structural Efficiency through Form</p><p>　　Of all traditional structural design elements (ranging from material</p><p>　　choice, profile sections, node ty

81、pe, global geometry, and support</p><p>　　conditions), global geometry mostly decides whether a shell will be</p><p>　　stable, safe, and stiff enough. The shell spans large distances with</p&

82、gt;<p>　　Fig. 2. Nuovo Polo Fiera Milano (Italy, built in 2004; architect Massimiliano Fuksas, structural engineers Schlaich Bergermann and Partner and Mero</p><p>　　TSK Group) illustrates how a sculp

83、tural shell is discretized in four-sided and triangulated (at the supports) meshes</p><p>　　Fig. 3. Hippo House (Germany, built in 1997), designed by architect Grieble and Schlaich Bergermann and Partners, s

84、hows the discretization of</p><p>　　a translational surface into planar quadrangular meshes (photograph courtesy of Edward Segal, reprinted with permission)</p><p>　　a fine structural network (s

85、keleton) of individual small subelements.</p><p>　　The first design consideration lies in setting the exact boundary</p><p>　　conditions within which the shell shape can be developed. The</p&

86、gt;<p>　　curved shape is of vital importance to achieve stability through</p><p>　　membrane stiffness. Shell bending needs to be avoided by finding</p><p>　　the “right” geometry, so that

87、under the self-weight only membrane</p><p>　　action results. Membrane action makes efficient use of material. The</p><p>　　important structural design challenge lies in the determination of</

88、p><p>　　a three-dimensional (3D) surface that will hold the skeletal shell.</p><p>　　In the twentieth century, both architects and engineers [Gaudi</p><p>　　(Huerta 2003), Otto (Otto e

89、t al. 1995), and Isler (Billington 2008)]</p><p>　　experimented with physical form finding techniques, which for</p><p>　　a given material, created a set of boundary conditions and gravity</p

90、><p>　　loading that found the efficient 3D structural shape. The importance</p><p>　　of finding a funicular shape for steel shells lies in the fact that the</p><p>　　self-weight (gravi

91、ty loads caused by steel and glass) contributes</p><p>　　largely to the load to be resisted. The subelements need to be loaded</p><p>　　axially to make most efficient use of the section profile.

92、</p><p>　　Numerical form finding techniques [force density (Schek 1974)</p><p>　　and dynamic relaxation (Day 1965)] have been successfully applied</p><p>　　to weightless systems who

93、se shape is set by the level of internal</p><p>　　prestress and boundary supports. However, when it comes to funicular</p><p>　　systems whose shape is not determined by initial prestress but<

94、/p><p>　　by gravity loads (such as the case for masonry, concrete, or steel</p><p>　　shells), fewer numerical methods have been developed. This is</p><p>　　mainly because of the diffic

95、ulty of finding optimal forms for those</p><p>　　shells that rely on both tensile and compressive membrane stresses</p><p>　　to resist dead load. Kilian and Ochsendorf (2005) presented</p>

96、<p>　　a shape-finding tool for statically determinate systems based ona particle-spring system solved with a Runge-Kutta solver, used in</p><p>　　computer graphics for cloth simulation. Block and Ochs

97、endorf</p><p>　　(2007) published the thrust network analysis to establish the shape</p><p>　　of pure compression systems. For the initial design competition for</p><p>　　the Dutch M

98、aritime Museum roof project, the dynamic relaxation</p><p>　　method usually used for prestressed systems was adapted to deal</p><p>　　with 3D funicular systems with tension and compression eleme

99、nts</p><p>　　under gravity loads.</p><p>　　Competition Design for a Steel Glass Shell over</p><p>　　the NSA Courtyard</p><p>　　The Dutch Maritime Museum planned a thoro

100、ugh museum renovation</p><p>　　in the near future. The restricted space in the seventeenth</p><p>　　century historic building hinders the movement of visitors. The</p><p>　　courtyar

101、d needed to be integrated into the museum’s circulation</p><p>　　space, sheltered from weather, and kept to a minimal indoor temperature.</p><p>　　An invited design competition was held for a ne

102、w glass roof</p><p>　　that added value to the historic building. In 2005, Ney and Partners,</p><p>　　a Brussels-based engineering design consultancy, won this competition</p><p>　　w

103、ith a steel and glass shell design. The shell manufacturing</p><p>　　and construction processes took place between 2009 and 2011. In</p><p>　　2012, the project was awarded the Amsterdam Architec

104、tural Prize.</p><p>　　Initial Planar Geometry</p><p>　　In the late seventeenth century, the historic building housing the</p><p>　　museum (shown in Fig. 4) was the headquarters of t

105、he admiralship. It was the instrument and symbol of the Dutch maritime power. The</p><p>　　development of this sea-faring nation was closely linked to the</p><p>　　production of sea charts and t

106、he associated sciences, such as geometry,</p><p>　　topography, and, astronomy. The classic building also uses geometry</p><p>　　as a basis for design. The choice for the initial two-dimensional