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Mathematical and numerical studies of shape sensitivity analysis in fracture problems.

Research Project

Project/Area Number 07640341
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHiroshima-Denki Institute of Technology

Principal Investigator

OHTSUKA Kohji  Hiroshima-Denki Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30141683)

Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1996: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1995: ¥300,000 (Direct Cost: ¥300,000)
KeywordsFracture problems / Stess intensity factors / Sensitivity analysis / Mathematical research / Numerical research / Computer language for finite element analysis / 数理工学 / 破壊力学 / 変分法 / 関数解析
Research Abstract

Stress intensity factors (abr. SIF) K are very important parameters in fracture mechanics which are characterized as the coefficient of the solution (displacement) of linear elastic system. SIF K depend on the shape of materials Omega, the shape of crack Sigma and the loads F,that is, K is the functional of {Omega, Sigma, F}. There are many researches on SIF by analyitical calculation, numerical results and experiments in individual cases, but systematic researches are few. In this research, we derive the formula which express the shape sensitivity analysis of SIF with respect to the shape of materials Omega. This formula is derived using the expression of SIF by dual singular solution technique and GJ-integral techique proposed by the author, which is given the R-integral expressin dR (u, Z) + (boundary integral). Here u is the solution, Z is the regular term of the dual singular solution, dR is the first variation of R-integral (area integral) of GJ-integral. If the solutions u and Z are regular on the perturbation, then we can change R-expression to P-expression (line-integral) by the fundamental property of GJ-integral that clarify the analytical property of the shape sensitivity. For the numerical analysis, we want to use the extension of the language for finite element method created by Prof. Pironneau Olivier et al. in France. Already we added the functions ; the area integral, line integtal, smooth cut-off functions and its partial derivatives.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] K.Ohtsuka: "Mathematical analysis of 3-D fracture phenomenon by Griffith's energy balance theory under increasing loads" Theoretical and Applied Mechanics. 45. 99-103 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka: "Fracture criterion and mathematical conjectures from fracture mechanics" Universitat Stuttgart,Sonderforschungsbereich 404, 42 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka, M.Bochniak: "Sensitivity analysis of stress intensity factors by generalized J-integrals" Universitat Stuttgart, Sonderforschungsbereich 404, 17 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka: "Mathematical analysis of 3-D fracture phenomenon by Griffith's energy balance theory under increasing loads" Theoretical and Applied Mechanics. 45. 99-103 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka: "Fracture criterion and mathematical conjectures from fracture mechanics" Universitat Stuttgart, Sonderforschungsbereich. 404,96/18. 1-42 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka and M.Bochniak: "Sensitivity analysis of stress intensity factors by generalized J-integrals" Universitat Stuttgart, Sonderforschungsbereich. 404,96/20. 1-17 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ohtsuka: "Mathematical analysis of 3-D fracture phenomenon by Griffith's energy balance theory under increasing loads" Theoretical and Applied Mechanics. 45. 99-103 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Ohtsuka: "Fracture criterion and mathematical conjectures from fracture mechanics" Universitat Stuttgart,Sonderforschungsbereich 404, 42 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Ohtsuka,M.Bochniak: "Sensitivity analysis of stress intensity factors by generalized J-integrals" Universitat Stuttgart,Sonderforschungsbereich 404, 17 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K. Ohtsuka: "Mathematical Aspects of Fracture Mechanics" Lecture Notes in Num. Appl. Anal.13. 39-59 (1994)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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