基于Hermite积分的非线性随机有限元法

A New Nonlinear Stochastic Finite Element Method Based on Hermite Integrate

将Hermite积分法应用于随机结构的有限元分析,针对非线性问题,建立基于Hermite积分法的随机有限元理论及列式。选择不同的Hermite积分点数目进行算例分析,并用Monte-Carlo法的计算进行对比研究,考察该方法的有效性。计算结果显示所提出的Hermite积分随机有限元有很高的计算效率,在精度上,3点积分在一阶矩、二阶矩计算上即有较高的精度,在选点数较多(如11个)时,三阶矩、四阶矩也有足够的精度。

We apply the Hermite integrate to nonlinear stochastic finite element method, and establish the theory and algorithm of Stochastic FEM based on the Hermite integrate. An example is put forward, which is solved by choosing different kinds of integrate points and verified with Monte-Carlo stochastic FEM. The result show that the new method own a high efficiency. On the precision, the first and the second order quadrature reach high precision although the integrate points only is 3, however, the high precision of the third and the fourth order quadrature need more integrate points (e.g.11).