【作者】 杨绿峰； 刘萍； 刘颖； 唐冲；

【Author】 Yang lufeng Liu ping Liu ying Tang chong (Department of civil and building engineering,Guangxi University,Nanning,530004)

【机构】 工程防灾与结构安全重点实验室,广西大学土木建筑工程学院；

【摘要】 摄动随机有限元法是小变异随机结构数值分析和可靠度计算的常用手段,对于具有较大变异系数的随机场,通常采用正交级数进行离散。本文在此基础上,利用随机减缩基将位移响应过程展开为随机场离散变量的函数,研究建立了减缩基随机有限元法,建立了结构随机分析的随机响应面法,并以将这些方法同摄动随机有限元、蒙特卡洛有限元法的计算情况进行了比较。研究结果表明,当随机场变异系数大于15%时,摄动随机有限元法的计算误差较大;而当随机场变异系数大于35%时,蒙特卡洛有限元法计算结果表现出不稳定性,误差较大。而减缩基随机有限元法和随机响应面法的计算结果始终表现出较好的精度和稳定性。而且减缩基随机有限元在处理大变异问题时,能够有效缩减控制方程的阶次,计算效率较高。另一方面,尽管随机响应面法和蒙特卡洛有限元法同属抽样模拟方法,但前者无论在计算精度、效率和稳定性方法,都具有很明显的优势。更多还原

【Abstract】 When the coefficients of variation (c.o.v) of the random field are small, perturbation stochastic finite element method (PSFEM) can be used for computing the statistical moment of response and reliability index.The orthogonal expansion can be used for decomposing the random field with large variation.Based on the orthogonal decomposition of the random field,this paper presents the reduced basis stochastic finite element (RBSFEM) and stochastic response surface method (SRSM) and makes comparison these methods with PSFEM and Monte-Carlo finite element method (MCFEM).For the problem considered,we find that when the c.o.v is greater than 15%,PSFEM is inaccurate;when the c.o.v is greater than 35%,MCFEM is unstable and inaccurate.But the RBSFEM and SRSM are always steady and accurate.It has been shown that the RBSFEM leads to a reduced-order deterministic system of equations with high efficiency.On the other hand,SRSM belongs to sampling method which is same as MCFEM,but SRSM is better than MCFEM with the accuracy,efficiency and stability.更多还原