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。

基本信息

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

项目摘要

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（简称SIF）K是断裂力学中非常重要的参数，它表征为线弹性系统的解（位移）系数。 SIF K 取决于材料形状 Omega、裂纹形状 Sigma 和载荷 F，即 K 是 {Omega, Sigma, F} 的函数。通过解析计算、数值结果和个案实验对SIF进行的研究较多，但系统的研究较少。在本研究中，我们推导了表达 SIF 相对于材料 Omega 形状的形状敏感性分析的公式。该公式是利用作者提出的对偶奇异解技术和GJ积分技术的SIF表达式推导出来的，给出了R积分表达式dR(u,Z)+(边界积分)。这里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）的第一个变体。如果解u和Z在摄动上是正则的，那么我们可以利用GJ积分的基本性质将R表达式改为P表达式（线积分），从而阐明形状敏感性的解析性质。对于数值分析，我们希望使用 Pironneau Olivier 教授等人创建的有限元方法语言的扩展。在法国。我们已经添加了这些功能；面积积分、线积分、平滑截止函数及其偏导数。