摘要
将随机有限元方法引入断裂分析中 ,考虑到裂纹尺寸的随机性 ,进行了J积分的随机分析。首先基于Tay lor级数展开的随机有限元方法 ,讨论了位移和应力的数字特征表示方法 ,指出位移和应力的偏导数计算是随机有限元的关键 ,并推导了位移和应力的偏导数计算公式以及刚度矩阵的偏导数和Jacob矩阵的偏导数的计算公式。然后推导了二维弹性J积分的随机有限元列式 ,编制了随机有限元程序。最后对程序进行了精度考核 ,与Monte carlo方法相比 ,误差为 0 3 5 %。
The fracture analysis which containing stochastic crack was discussed. Using the stochastic finite element method of Taylor′s expansio n , the stochastic equivalent partial equation was established, and the partial de r ivatives of displacement and stress and the stiffness matrix and the Jacob′s ma tr ix were derived. Consequently, the partial derivative of J -integral was der ived. B ased on these formulas, the related program was carried out by the author, which was proved by some numerical examples. It is shown that the result error is abo ut 0.35% which is compared with Monte-carlo method.
出处
《南京化工大学学报》
2001年第4期21-23,共3页
Journal of Nanjing University of Chemical Technology(Natural Science Edition)
