在考虑材料参数、裂纹长度、外载分散性的前提下,文中用Taylor展开随机有限元方法分析平面裂纹应力强度因子分散性。首先用一般六结点单元和六结点奇异等参单元建立平面裂纹的有限元模型,接着推导随机有限元方法用到的位移偏导数和刚度矩阵偏导数的表达式,最后给出在各随机因素影响下的应力强度因子均值和方差的计算公式,并将计算结果与Monte Carlo法模拟结果进行对比。算例结果显示,材料弹性模量、外载、裂纹长度的分散性对应力强度因子的分散性影响比较显著,而材料泊松比影响很小。
Taylor stochastic finite element method(TSFEM) is applied to analyze the uncertainty of plane crack stress intensity factor(SIF) considering the uncertainty of material properties and crack length and load.Finite element model of plane crack is presented.In the model,crack tip is meshed by using six-node triangular quarter-point elements;and other area is meshed by using six-node triangular elements.The partial derivatives of displacement and the stiffness matrix used by TSFEM are derived.The mean and varia...