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空間構造の幾何学特性と力学挙動に関する研究

空间结构几何特性与力学行为研究

基本信息

批准号：
10J09407
负责人：
三木優彰
金额：
$ 0.9万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2010
资助国家：
日本
起止时间：
2010 至 2011
项目状态：
已结题

项目摘要

博士課程3年間の研究内容を博士論文にまとめ、「三項法と双対推定による構造物の釣り合い形状の探索」と題し、工学系研究科建築学専攻へ提出を行った。実数値関数の停留値問題、仮想仕事の原理、勾配記号∇を用いた停留条件の3つの一般表現を中心に、構造物の釣り合い形状の探索に利用可能な問題の表現を整理した。また、張力構造の形状決定問題及び連続体の大変形問題を、勾配ベクトルの一般化という観点から統一的に扱える枠組みを整備した。定式化の特徴としては、歪の代わりにリーマン計量を用い、変位場を用いない、次元に非依存などの特徴がある。また、材料則としては弾性体のみを扱う。さらに、標準的な関数の直接最小化及び束縛条件つき最小化として、三項法と双対推定が構造物の釣り合い形状の探索という目的に適していると論じた。ここではユークリッド空間上のみならず、リーマン多様体上での最小化の定式化を行った。逐次二次計画法や直線探索を用いた方法との比較も行った。さらに、構造デザインの視点にたち、減衰定数γ=0.98の提案及び、実際の構造物の設計にどのように利用可能か詳細にスタディを行った。例えば、テンセグリティ、張力膜構造、ケーブルネット構造、特に、リアルタイムな入力デバイスと高精度な可視化デバイスの利用を前提に、繰り返し計算の途中で各種パラメータを変更可能なフローチャートの提案と、多様な問題の釣り合い形状の探索の様子の図示を行った。また、付録に曲面論やリーマン幾何、連続体の力学、膜理論などをまとめた。

In the past 3 years, the Ph.D. has studied the contents of the doctorate, the "three-project method, the double method, the exploration of the shape of the creation, the exploration of the shape," and the research program of the department of engineering. The question of how to count and stay, the principle of "thinking about things", the matching of symbols, the use of conditions of stay, the center of general representation, and the exploration of the shape of creation, the use of possible problems to show and organize. In order to solve the shape determination problem and the large shape problem of the system, and to configure the system that generalizes the system point system of the system, the system of the whole system. Format the special data, distort the data, use the data, the data is independent, and the data is not dependent. Materials, materials and materials. The direct minimization of the number of figures and standards, and the two-way presumption of creation, the combination of shapes and the purpose of the three-item method are directly minimized and discussed. Please make sure that you can make sure that you can make sure that you do not want to make any changes in the space, and that you need to minimize the number of lines on your computer. The successive quadratic drawing method "straight line exploration" is used to compare the lines with the method of linear analysis. The proposal that the number of points, the decay number γ = 0.98, and the design of the international instrument of creation should be used in order to make use of the possibility to improve the performance of the system. For example, for the production of mechanical films, for example, for the production of mechanical films, for example, for the production of mechanical films, for example, for the manufacture of mechanical films, for example, for the production of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, for example, for the manufacture of mechanical films, The theory of surface, the mechanics of connectors, and the theory of membrane.