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

断裂问题中形状敏感性分析的数学和数值研究。

• 批准号: 07640341
• 负责人: OHTSUKA Kohji
• 金额: $ 0.38万
• 依托单位: Hiroshima-Denki Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640341/
• 关键词: Fracture 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

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.

应力强度因子（abr.应力强度因子K是断裂力学中非常重要的参数，它表征了线弹性体系的解（位移）系数。应力强度因子K取决于材料的形状Ω、裂纹的形状σ和载荷F，即K是{Ω，σ，F}的泛函。目前对应力强度因子的研究主要是通过解析计算、数值计算和实验等方法进行的，但系统的研究较少。在本研究中，我们推导出应力强度因子对材料形状Ω的形状敏感性分析公式。利用对偶奇异解技术和作者提出的GJ积分技术，导出了应力强度因子的表达式，给出了dR（u，Z）+（边界积分）的R积分表达式。其中u是解，Z是对偶奇异解的正则项，dR是GJ积分的R积分（面积积分）的第一变分。如果解u和Z在扰动下是正则的，那么我们可以利用GJ积分的基本性质将R-表达式转化为P-表达式（线积分），从而阐明形状灵敏度的解析性质。对于数值分析，我们希望使用法国Pironneau Olivier教授等人创建的有限元法语言的扩展。我们已经添加了函数;面积积分，线积分，光滑截止函数及其偏导数。

项目成果

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)

K. Ohtsuka：“根据格里菲斯能量平衡理论对载荷增加时的 3-D 断裂现象进行数学分析”理论与应用力学 45. 99-103 (1996)。

K.Ohtsuka: "Fracture criterion and mathematical conjectures from fracture mechanics" Universitat Stuttgart,Sonderforschungsbereich 404, 42 (1996)

K.Ohtsuka：“断裂力学的断裂准则和数学猜想”Universitat Stuttgart，Sonderforschungsbereich 404, 42 (1996)

K.Ohtsuka, M.Bochniak: "Sensitivity analysis of stress intensity factors by generalized J-integrals" Universitat Stuttgart, Sonderforschungsbereich 404, 17 (1996)

K.Ohtsuka、M.Bochniak：“广义 J 积分对应力强度因子的敏感性分析”Universitat Stuttgart，Sonderforschungsbereich 404, 17 (1996)

K.Ohtsuka: "Fracture criterion and mathematical conjectures from fracture mechanics" Universitat Stuttgart, Sonderforschungsbereich. 404,96/18. 1-42 (1996)

K.Ohtsuka：“断裂力学的断裂准则和数学猜想”斯图加特大学，Sonderforschungsbereich。