1996 Fiscal Year Final Research Report Summary
Mathematical and numerical studies of shape sensitivity analysis in fracture problems.
| Project/Area Number |
07640341
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima-Denki Institute of Technology |
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Principal Investigator |
OHTSUKA Kohji Hiroshima-Denki Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30141683)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Fracture problems / Stess intensity factors / Sensitivity analysis / Mathematical research / Numerical research / Computer language for finite element analysis |
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| 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.
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Research Products
(6 results)
