基于K-L级数的改进摄动随机QR法

K-L series based modified perturbation stochastic QR method

为了有效对具有随机参数的平面框架结构进行随机分析,提出基于Karhunen-Loève (K-L)级数的改进摄动随机QR法(KLSMPSQRM).使用Karhunen-Loève级数展开法对随机场进行离散,同时引入QR法替换改进的摄动随机有限元法(MPSFEM)中的有限元计算格式,得到一种兼具三种方法优势的新型随机分析方法.通过计算多层平面框架,将KLSMPSQRM与其他方法进行对比,结果表明:QR法具有良好的精度与适用性,可以代替有限元法进行计算;KLSMPSQRM在变异系数小于0.25的条件下可以保证一定精度,应用范围较传统的摄动随机有限元法更广,同时兼顾了计算效率,是一种有效的框架结构随机分析手段.

To effectively analyze the plane frame structures with random parameters,a Karhunen-Loève (K-L) series based modified perturbation stochastic QR method (KLSMPSQRM) was proposed.The K-L series expansion method was used to discretize random fields,and QR method was introduced to replace the finite element calculation procedures of modified perturbation stochastic finite element method (MPSFEM),and a new stochastic analysis method with the merits of the three methods was obtained.By calculating the multi-layer plane frame,KLSMPSQRM was compared with other methods.Results show that the QR method has good accuracy and applicability,and can replace finite element method;KLSMPSQRM can maintain good accuracy in the case that coefficient of variation is less than 0.25,which has a wider application range than the conventional perturbation stochastic finite element method;meanwhile,the calculation efficiency of KLSMPSQRM is also high,and therefore KLSMPSQRM is an effective means for the stochastic analysis of frame structures.