a-N曲线的微分方程拟合法  

DIFFERENTIAL EQUATION FITTING METHOD OF A-N CURVE

作　　者：郑荣跃[1] 徐永春[1] 林安珍[1] 

机构地区：[1]宁波大学建筑工程与环境学院,宁波315211

出　　处：《钢结构》2004年第6期31-33,共3页Steel Construction

基　　金：浙江省教育厅资助项目 (编号 :2 0 0 2 417)。

摘　　要：钢结构节点的疲劳裂纹扩展研究中 ,为了使裂纹扩展速率分散性尽可能小 ,需要高精度地拟合疲劳裂纹扩展a -N曲线。通过将试验得到的裂纹扩展数据 (ai,Ni) (i =1,… ,n)为一不等间距的时间序列 ,利用灰色建模的思想 ,用改进的不等间距的时间序列灰色微分方程GM(1,1)模型拟合a-N 试验曲线。进一步观察发现 ,a-N 曲线的形状与翻转 180°的S-N 曲线形状相似 ,由此引出拟合a-N 关系的四参数经验公式 ,四个参数用结合优化技术的微分方程拟合法估计。计算表明 ,基于微分方程模型的四参数拟合法拟合精度较高 。For reducing variability and dispersion of the growth rate of fatigue crack,the a-N test data of crack propagation should be fit ted by high precision formula.In t his paper,it is considered that fa tigue crack propagation is governe d by differential equation,the met hod of differential modelling is pr oposed to fit a-N test data and to determine the growth rate of fatig ue crack.Further,it is discovered that a-N curve rolling 180° is sim ilar to S-N curve in shape.Therefo re,a four-parameter formula fittin g a-N curve is proposed,in which t he unknown parameters can be obtai ned by the method of differential m odelling.It is indicated that the f our-parameter formula give high f itting precision,and is consistent to the experimental result satisfactorily.

关 键 词：a-N曲线 微分方程拟合法 钢结构 疲劳裂纹扩展 

分 类 号：TU391[建筑科学—结构工程]