基于响应面的三维随机有限元法在大型结构可靠度分析中的应用

Application of 3-D stochastic FEM based on response surface in large structure reliability analysis

工程中大型、复杂结构的极限状态方程与输入随机变量的关系往往是未知的,利用响应面法,用一个二次多项式来模拟结构的极限状态方程.首先利用中心复合设计技术获得有关输入随机变量的多组试验点,用这些试验点分别调用有限元程序,可得到相应的多组输出随机变量;然后由已获得的输入、输出随机变量,用最小二乘法来估计二次多项式的参数,即可得到极限状态方程的一个合理近似式;最后用结构可靠度分析中的几何法来计算可靠度指标.对一个重力坝的建基面抗滑稳定可靠度以及坝体单元的可靠度进行了研究,得到了一些重要的结论,指出了提高可靠度指标的途径.算例表明了该方法的有效性.

The relation between the limit state function of large and complex structural systems and input random parameters is always unknown. A quadratic polynomial is considered to simulate the physical limit state function. Firstly, the experimental points of the input random parameters are determined by central composite design and the output random parameters are obtained by finite element method in which value of the experimental points are cited. Secondly, the unknown parameters of a quadratic polynomial are defined by regression analysis and a reasonable approximation of the physical limit state function is obtained. Finally, reliability index of the approximation is evaluated by geometric method in structural reliability analysis. The reliability of the construction foundation surface against sliding and element reliability of gravity dam are studied. Important conclusion is drawn. Example shows that the suggested method is effective.