摘要
基于函数的正交分解、次序正交分解与区间数学理论,推导出区间扩阶系统方程,并利用不确定性结构分析的扩阶系统方程对具有不确定性参数的结构系统进行静力分析。将不确定参数处理为有界区间数,基于有限元模型和区间结构力学矩阵的线性分解形式,通过区间扩阶系统方程和有约束的非线性优化方法,对具有区间参数的结构静力响应进行计算。通过数值算例,对区间扩阶系统方法的结果与解析结果进行对比,分析了区间扩阶系统的展开阶数和不确定度对计算结果的影响,数值结果表明了区间扩阶系统方法的可行性与有效性。
Based on the orthogonal and order orthogonal decomposition of a function and interval mathematics, obtain the interval expanded order system method. In this paper, analyze the static response of structure with uncertain parameters by use of the expanded order system equation. An uncertainty parameter is treated as a bounded interval. Based on the finite element model and linear representation of a mechanics matrix of an uncertain structure, taking the advantage of an extended order system method, obtain the static responses of a structure with interval parameters. Finally using a numerical example, we compare the results with the exact ones, and then we discuss the influence of the order of expansion and uncertainty. The results show that the feasibility and effectiveness of the interval extended order system method.
出处
《工程力学》
EI
CSCD
北大核心
2013年第1期22-30,共9页
Engineering Mechanics
基金
国家自然科学基金项目(11002013)
高等学校学科创新引智计划项目(B07009)
国防基础科研计划项目(A2120110001
B2120110011)
关键词
次序正交分解
区间扩阶系统
不确定性
区间方法
静力响应
order orthogonal decomposition
interval extended-order system
uncertainty
interval methods
static response
