| Project/Area Number |
10205214
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | Kyoto University |
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Principal Investigator |
KATOH Naoki Kyoto Univ., Dept. Architecture and Architectural Systems, Professor, 工学研究科, 教授 (40145826)
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| Co-Investigator(Kenkyū-buntansha) |
FUJISAWA Katsuki Kyoto Univ. Dept. Architecture and Architectural Systems, Research Associate, 工学研究科, 助手 (40303854)
TAGAWA Hiroshi Nagoya Univ., Dept. Architecture, Associate Professor, 工学研究科, 助教授 (70283629)
OHSAKI Makoto Kyoto Univ., Dept. Architecture and Architectural Systems, Associate Professor, 工学研究科, 助教授 (40176855)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥10,500,000 (Direct Cost: ¥10,500,000)
Fiscal Year 2000: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1999: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1998: ¥4,600,000 (Direct Cost: ¥4,600,000)
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| Keywords | optimal topology / semidefinite program / triangular mesh generation / optimal room layout / computational geometry / orthogonal graph drawing / 直線成分 / 三次元モデル再構成 / トポロジー最適化 / 半正定値計画 / 三角形メッシュ / 三角形分割 / 形状最適化 / kレベル解析 / 最適構造設計 / 階層的簡略化 |
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| Research Abstract |
The results obtained are summarized as follows.
1. We consider the problem of generating triangular meshes for planar regions and a class of curved surfaces using Steiner points that minimizes the maximum edge length ratio under the constraint that (1) the number of Steiner points are given or (2) the lower bound on minimum edge length is given. We have developed algorithms for the problem.
2. Truss topology optimization problem for specified fundamental frequency has been shown to be formulated as SemiDefinite Programming (SDP) problem. An optimal topology with five-fold fundamental frequencies has been obtained without any difficulty. General forms of necessary and sufficient optimality conditions have been derived from the optimality conditions of the SDP problem, and the symmetry properties of optimal topologies have been investigated. It has also been shown that optimal solutions under linear buckling constraints can be found by successively applying SDP.
3. Large-deformation analysis problem of cable networks has been formulated as Second-Order Cone Programming (SOCP) problem. It has been demonstrated that equilibrium shapes can be found without any even for an unstable equilibrium state.
4. The design of room layout is determined by the adjacency of room, room size, shape, orientation and etc. We formulated the problem of optimal room layout as a mathematical programming problem from the viewpoint of geometric optimization. We have developed a new algorithm for the problem using orthogonal graph drawing algorithms.
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