基于K-L级数的改进摄动随机QR法  

K-L series based modified perturbation stochastic QR method

作　　者：李秀梅[1,2,3] 邵湛钧 张永兵[1,2,3] 李朝阳[4] LI Xiumei;SHAO Zhanjun;ZHANG Yongbing;LI Zhaoyang(College of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;Key Laboratory of Engineering Disaster Prevention and Structural Safety of Ministry of Education,Guangxi University,Nanning 530004,China;Guangxi Key Laboratory of Disaster Prevention and Engineering Safety,Guangxi University,Nanning 530004,China;Guangxi Polytechnic of Construction,Nanning 530007,China)

机构地区：[1]广西大学土木建筑工程学院,广西南宁530004 [2]广西大学工程防灾与结构安全教育部重点实验室,广西南宁530004 [3]广西大学广西防灾减灾与工程安全重点实验室,广西南宁530004 [4]广西建设职业技术学院,广西南宁530007

出　　处：《华中科技大学学报（自然科学版）》2021年第7期19-23,36,共6页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51868004);广西自然科学基金资助项目(2013GXNSFBA019236)。

摘　　要：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.

关 键 词：随机场 Karhunen-Loève级数展开法 改进的摄动随机有限元法 QR法 随机分析 

分 类 号：TU311.41[建筑科学—结构工程]