別紙41 (課程博士(英文))Date of submission (1nonth day, year)ν12/2018

Dcparlment
DeP舐'tment of AI'chitccture

StudcnuD Number

D159501
Supervisofs

and civil En部neenng
Pplicanl's nameShojiNakazawa
Taikisa北0
Yukihiro Matsumoto

YujiTakiuchi

Abstract (Doctor)
Study on Design Method ofFree・Fonn Reticulated sheⅡ Str11CtU↑es considerino Bucklino
Ti11e ofThesis

and vibration

U墾屈と振動をぢ慮した自由曲面ラチスシェルの設計法に関する研究)
Approx.80o words

Reticulated she11Structures are constituted by arrangin牙 elon牙ated members in a mesb form,
and one of the typical structures of a spatial structure.1n 今eneral, its bucklin曾 andVibrational properties are compHcated, and it is known that the mechanical properties chan旦edrastica11y depending on the shape of the she11. For this reason, mechanical properties anddesign methods have been studied one by one for each shape of a dome, a cylinder, ahyperbolic parab010id by many researchers. And simple desi曾n methods are bein牙

established. on the other hand, due to the development of 3DCAD, construction techni ues,and morph0宮enesis techniques in recent years, a sheⅡ With a complicated 又eometry ca11ed

free、form reticulated she11 has attracted attention. The number of cases where the free・form
reticulated sheⅡ is used for designin曾 Sports arenas, museums, and commercial facilities isincreasin牙. However, there are many unexplained points about the structural performanceand the ultimate S訂'ength of the free、form Teticulated she11S、 Therefore, in practice,北 isnecessary to perform so many FEM analyzes considerin宮 material nonlinearity a口d曾eometrical nonlinearlty as opposed to a spherical dome, etc. And it is required to construct aSimple desi宮n method.

From the above back牙round, in this reseaych, buckHng behavior and Selslnlc responses areinvestigated as a fundamental research for estabHshin牙 the structura] design method of thefree、form reticulated she11 Structures.1n addition, optimization methods consid田,ing bucklin牙
and seismic response to determine the shape ofreticulated she11 Structures are proposed、The content ofeach chapter is summarized as f0ⅡOWS.

In the lst chapter, the background and objectives of this study are described、In the 2nd chapter, the buckling behavior and the seismic responses are investi今ated. The
Shape of the reticulated she11 roof is determined by shape optimization analysis aimin又 atminimizin号 the stress a牙ainst the dead load. The elastic buckHn牙 analysis and theelasto、plastlc buckling analysis are carried out in consideration of 曾eometricalimperfections.
It is clarified that the evaluation method for ultimate stren牙th proposed for domical and
Cylindrical reticulated she11S can be applied to the free・form reticulated she11.1n the d namicbehavior, a lar牙e vertical displacement is observed against the horizontal eaTthquake input,
and the necessity of the shape optimization method considering the earthquake 訊7asConfirmed.

In the 3rd chapter, a shape optimization method that maximizes the buckling strength Of
free、form reticulated she11 Structures. specificaⅡy, maximization of the estimated value Of

bucklin又 Strength applyin曾 the evaluation method investigated in the 2nd chapter isProposed.1n addition, maximization of the initial yield load is also proposed、 The strainenergy minimization and the linear buckHng load maximization proposed past research areCωlied out respectively. These optimization analyzes are Performed using genetic
algor北hms. From the comparison of the ultimate strength ofthe shapes obtained b the four
Optlmizations, it is C1砥'ified that the proposed method haS 今ood performance.
In the 4th chapter, the seismic responses of free"form reticulated she11S are investi ated b

Paying attention to the response of only the roof structure. The shape optilnization method

Considering the seismic load is proposed. From the time history analysis of the obtained
Shape, the validity of the proposed optimization method is confirmed. Furthermore, design
Problems are clarified considerin曾 the critical deformation of the members.

In the 5th chapter, the seismic responses of the free'form reticulated she11S supported by theSubstructure are analyzed、 The shape of roof structures are 牙enerated by two kinds of shape
Optimization. one is generated by minimizin宮 the strain energy with respect to the dead load,
and the other iS 宮enerated by solving the two objective optin〕ization problem for the dead load

and the horizonta110ad. Then a lnethod for calC111ating a static seismic load simulatin曾 theelastic response of the structure lvith two dominant vibrational modes is proposed. The
dominant vibrational mode is analyzed from eigenvalue analysis. The accuracy of theProposed method is discussed fTom the comparison of static analysis using the seismic load
and time history response analysis.
In the 6th chapter, the summary of the present study is described.

月噺妖42 (課程博士(手U文))
平成

建築・都市システム学専攻
氏空,

学士条曾番・号・

第 159501号

指導教員

滝内雄二

2 9年

1月

中澤

1羊二

齊財i大樹松本幸大

1 2日

論文内容の要旨(博士)
座屈と振動を老慮した自由曲面ラチスシェルの設計法に関する研究
陣士学位論文名(study on Design Method ofFI'ee・Form Reticulated sheⅡ Stl'uctures considering Bucklin
and vibrati0川(要旨 1,200字程度)

入きな無柱空問を稜う柚造形式のーつとして,細長い告剛オを網目状に配置して曲面を仟成すブーチ,スシエル構造がある。一般にラチスシェルは座屈や而打喪設計においてその挙動が複雉であることが知られ,シエルの曲面形状によってその大きく変化することが知られてぃる。このため,これまで球形,円筒, HPといった形状ごとにその力学的性状や設計法の靭ヲモが進められ,簡戸な計算を基に広居耐ブや而W1陛能を評価する設計手法が確立しっっある。一方,近午の 3DCADやBⅨなどの兆'圭に支、られ,・契雑な曲面形状を有する内由岫而ラチスシェルに注目が集まり,建設事伊仂江畄えてぃる。し六しメバら,

自由曲而ラチスシェルの構造性能にっいては不明な点が多く,構造検討では材料.ヲ畔泉形性や,幾何非線汗多陛をぢ慮したF獣U弊析を多数行う彪、要があり,簡易な設.十手法の確立が求められてぃる。

以上の背景より,本研究では自由曲而ラチスシェルの構造設斗法確立のための基伊nリ研九とし,腔り鵬挙動,地震応答に対する検剖ブ丁法,さらに日本のような災害が多発する地域での自d Ⅱrーチズ
エル汗会伏の決定方法の提案が本論文で行われている。本楡文の内容は全6章により槽成されてぃブ。
各章の要約を以下に示す。

第1章では,本研究の背景とE1的を述べてぃる。

第2章では,固定荷重下の応力最小化を励杓として自由曲而ラチスシェルを形状最高化により生成し,得られた形状に対して座j譜陛状,地震応答性状を分析した。座屈解析より既往の球や円竹形状のーチスシエルに用いられる座屈而リJ評価乎法が向HH愉面に対'しても適用可彬であること を示した。また,
地震1古答角測折からは水平方向の地震入力に対して過大なr画亦位が発生すること を耐疏忍し,地震の多い地域での設計では地震を老應した形状決定や構造設計手法の必戸陛を確契した。

第3章では,ラチスシェルの座屈耐力を最大化tる手法を提突した。貝イ本的には2告で砕契した耐力諄価法用いた耐力の推定値最大化と,初期降伏荷重の最大化を提案した。既往の研九で"安された手法と提案手法の座屈耐力の比較より,耐力の推定値最大化が優れた性伊を有すブことを明らブ、にした。

第4章では,自由曲面ラチスシェルの地震兄之村生状にっいて,屋根剖如)みのj十答に注目し右予・た。
地震荷重を芳慮したラチスシェルの形状最適化手法を提案した。得られた形状の地手j六答"析よV1貝安手法の妥当性を磁瓢忍するとともに,音院オの限界変形の分析より,ル,十上d并拐題点を明らかにした。
第5章では,下音酢俸造を有する自由山而ラチスシェル地震応答性状をハイfした。圖下振到佃f 、、 2個の卓越モードを有している形状にっいて静的地震荷重の算出ブ"去を提突し,地震式答修杠か、その特度を明らかにした。

第6章では,本研究を通して得られた結果を総括し△伊の研ヲ嘘果題を示した。