利用积分随机有限元计算结构可靠度

积分随机有限元是一种新型随机有限元,它利用确定性有限元实现随机分析。本文首先利用积分随机有限元得到结构功能函数的各阶矩,通过Gram-Charlier级数拟合得到结构功能函数的概率密度函数,最后利用数值积分计算出结构的可靠度。作为对比,利用直接Monte-Carlo法模拟对结果进行验证,结果表明,本方法利用较少的积分点即可得到较高的计算精度,且随机变量可服从任何分布,与其它的可靠度计算方法相比具有一定的优势。

Applying Integral Stochastic Finite Element Method (ISFEM) to Calculating Structural Reliability

The integral stochastic finite element method(ISFFM) is a new variety of stochastic finite element method that performs,stochastic analysis by using the deterministic finite element.The paper employed the ISEEM to obtain the every order moment of a structural function,then its probability density function by fitting the Gram-Charlier series.Finally it calculated structural reliability using numerical integrals.In contrast,it used the direct Monte-Carlo method to perform a simulation and verify the above-mentioned results.The simulation results indicate that the ISFEM uses smaller integral points than other methods but obtain higher calculation accuracy and that the stochastic variants thus obtained obey distribution of any types,possessing several advantages compared with other reliability calculation methods.