一种新型随机有限元法

A New Method of Stochastic Finite Element

将Legendre积分法应用于随机结构的有限元分析,针对多随机变量非线性问题,建立基于Legendre积分法的随机有限元算法及列式。选择不同的Legendre积分点数目进行算例分析,并用MonteCarlo法的计算进行对比,考察该方法的有效性。计算结果显示,单随机变量问题在很少样本点的情况下,一阶矩、二阶矩既有较高的精度,在选点数较多时,多随机变量问题的一阶矩、二阶矩也有足够的精度。考虑到计算上有很高的效率,该方法在随机有限元的计算上具有一定的价值。

Appling the Legendre integrate method into multi random variables nonlinear stochastic finite element method, a new stochastic FEM algorithm was established. Examples are put forward, using different sorts of integrate points and verified by Monte Carlo stochastic FEM. The result shows that for single random variable, the first、second order moment reach high precision although the integrate points is fewer; for multi random variables, the precision of the first、second order moment is acceptable on the condition of relatively more points. Considering the high efficiency, the new stochastic finite element method is a valuable algorithm.