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エネルギー逸散・接触を伴う建築構造物の錐相補性条件に基づく高精度非線形解析法

Research Project

Project/Area Number 17760453
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Building structures/materials
Research InstitutionThe University of Tokyo (2006-2007)
Kyoto University (2005)

Principal Investigator

寒野 善博  The University of Tokyo, 大学院・情報理工学系研究科, 講師 (10378812)

Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords対称錐 / 相補性問題 / 接触問題 / クーロン摩擦 / 不安定現象 / 弧長法 / 不確定性 / 数理計画法 / 対称錘 / 孤長法
Research Abstract

平成19年度は,以下に示すように,構造物の様々な応答量の不確定性に注目し,錐相補性条件に基づいて応答量のばらつきを評価する数値手法を開発した。
[1]構造物が受ける外乱の大きさや方向を正確に予測することは,本質的に困難である.また,現実の構造物は,解析モデルとは異なり,施工誤差や損傷などの影響を受けるため,その剛性は不確定である.本研究では,構造物の剛性と構造物に作用する外力の双方が非確率論的な不確定性モデルに従ってばらつくときに,構造物の応答のばらつきを安全側で評価する手法を提案した.特に,変位や応力などの静的な応答量のばらつきを,外側から近似する楕円体を求める手法を開発した.錐相補性条件を用いることで,このような楕円体は半正定値計画問題を解くことで得られることを示した.また,従来の区間解析で用いられる区間は1次元上の楕円体とみなせるため,提案手法は通常の区間解析の枠組を特別な場合として含むことを示した.本研究および関連研究の成果は,2編の論文として国際誌および英文編著に掲載された.
[2]本研究では,トラスに作用する外力が不確定な場合に,塑性崩壊荷重のばらつきを評価する数値手法を提案した.特に,死荷重と参照外乱の2種類の外力を考え,死荷重が非確率論的な不確性を有することを仮定する.このとき,塑性崩壊荷重の最小値を最悪塑性崩壊荷重と定義し,その値を求めるための混合整数計画問題を定式化した.さらに,分枝限定法および離接カットを用いて最悪塑性崩壊荷重を求めるためのアルゴリズムを提案し,数値実験によりその有効性を確認した.本研究および関連研究の成果は,1編の論文として国際誌に掲載された.

Report

(3 results)
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (12 results)

All 2008 2007 2006

All Journal Article (9 results) (of which Peer Reviewed: 2 results) Presentation (2 results) Book (1 results)

  • [Journal Article] Worst-case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming2007

    • Author(s)
      Y. Kanno and I. Takewaki
    • Journal Title

      Journal of Mechanics of Materials and Structures 2

      Pages: 245-273

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ellipsoidal bounds for static response of framed structures against interactive uncertainties2007

    • Author(s)
      Y. Kanno and I. Takewaki
    • Journal Title

      Interaction and Multiscale Mechanics: an International Journal 1

      Pages: 103-121

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Robustness analysis of trusses with separable load and structural uncertainties2006

    • Author(s)
      Y.Kanno, I.Takewaki
    • Journal Title

      International Journal of Solids and Structures 43

      Pages: 2646-2669

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Are-length method for frictional contact problems using mathematical programming with complementarity constraints2006

    • Author(s)
      Y.Kanno, J.A.C.Martins
    • Journal Title

      Journal of Optimization Theory and Applications 131

      Pages: 89-113

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Confidence ellipsoids for static response of trusses with load and structural uncertainties2006

    • Author(s)
      Y.Kanno, I.Takewaki
    • Journal Title

      Computer Methods in Applied Mechanics and Engineering 196

      Pages: 393-403

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Sequential semidefinite program for maximum robustness design of structures under load uncertainties2006

    • Author(s)
      Y.Kanno, I.Takewaki
    • Journal Title

      Journal of Optimization Theory and Applications 130

      Pages: 265-287

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem2006

    • Author(s)
      Y.Kanno, J.A.C.Martins, A.Pinto da Costa
    • Journal Title

      International Journal for Numerical Methods in Engineering 65

      Pages: 62-83

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Arc-length method for frictional contact problems using mathematical programming with complementarity constraints2006

    • Author(s)
      Y.Kannno, J.A.C.Martins
    • Journal Title

      Journal of Optimization Theory and Applications 131(掲載予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Contact analysis of cable networks by using second-order cone programming2006

    • Author(s)
      Y.Kanno, M.Ohsaki
    • Journal Title

      SIAM Journal on Scientific Computing 27

      Pages: 2032-2052

    • Related Report
      2005 Annual Research Report
  • [Presentation] Global optimization algorithm for worst-case limit analysis of trusses under load uncertainties2007

    • Author(s)
      Y. Kanno and I. Takewaki
    • Organizer
      The 4th International Conference on Computational Methods (ICCM 2007)
    • Place of Presentation
      広島
    • Related Report
      2007 Annual Research Report
  • [Presentation] Confidence bounds for static response of braced frames with structural and load uncertainties2007

    • Author(s)
      Y. Kanno and I. Takewaki
    • Organizer
      The 3rd Asian-Pacific Congress on Computational Mechanics (APCOM'07)
    • Place of Presentation
      京都
    • Related Report
      2007 Annual Research Report
  • [Book] Y. Tsompanakis, N.D. Lagaros, and M. Papadrakakis (eds.), Structural Design Optimization Considering Uncertainties2008

    • Author(s)
      Y. Kanno and I. Takewaki
    • Publisher
      Maximum robustness design of trusses via semidefinite programming
    • Related Report
      2007 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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