Legendre积分法在随机有限元法中的应用

将Legendre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Legendre积分法的随机有限元列式。选择不同的Legendre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。计算结果表明本文提出的Legendre积分随机有限元有很高的计算效率，在精度上，较少的积分点在一阶矩、二阶矩计算上即有较高的精度，在积分点数较多时，三阶矩、四阶矩也有较高的精度。

Application of Legendre integrate in stochastic finite element

Applyng the Legendre integrate into nonlinear stochastic finite element method, establish the algorithm of Stochastic FEM based on the Legendre integrate. Examples are solved by choosing different kinds of integrate points and verified by Monte-Carlo stochastic FEM. The result shows that the new method is of a high efficiency. For the precision, the first and second moment reach high precision although the integrate points is fewer, however, the high precision of the third and fourth moment need more integrate points.