随机有限元方法在断裂分析中的应用

在幂律非线性随机有限元基础上，以单边裂纹板为例给出计算含量钢继裂参数，J（J积分），δ（裂纹张开位移），Δ（由裂纹引起的裂纹板上下底面相对位移），θ（由裂纹引起的裂纹板上下底在相对转角）及其对基本随机变量变化率的方法和分析算例。

Stochastic finite element method in engineering fracture analysis

When fracture porbability analyses for a structure is done, it is necessary to compute the mean values and variances of fracture parameters. The mean values can be calculated by normal finite element method while to calculate the variances needs by using stochastic finite element method. In this paper a method has been introduced by which the engineering fracture analysis can use a penalty stochastic finite element. First the formulae are given which can be used to calculate the fracture mechanics parameters of a single edged crack plate by means of stochastic finite element method. The fracture mechanics parameters include the J-integral and the crack opening displacement and the relative displacement and angle of rotation of upper and lower of the plate, as well as their derivatives with respect to a basic stochastic variable. The derivatives in the fracture mechanics parameters calculations, such as derivatives of the displacements, the strains as well as stresses, are calculated by a nonlinear penalty stochastic finite element method used in powerhardenging material.Then a differential method is introduced to test the results calculated by the stochastic finite element method.In the end, some computation examples of engineering fracture analysis are given including elastic fracture analysis and fully plastic fracture analysis. In the elastic fracture analysis the crack length is as a basic stochastic variable and in fully plastic fracture analysis the crack length and the power index are as basic stochastic variables.