基于区间分析的工程结构不确定性研究现状与展望

随机分析方法、模糊分析方法是已经广泛使用的工程结构不确定性分析方 法, 近年来区间分析方法逐渐为人们所熟知并成为是一种新的工程结构不确定性分析方法, 它主要用来研究具有区间特性的工程结构. 区间分析方法在统计信息不足以描述不确定参数 的概率分布或隶属函数、工程单位仅提供不确定参数的区间范围而想获得结构响应的区间范 围时就发挥了其优点. 综述了区间分析方法及其在工程结构不确定性分析中的应用状 况, 将基于区间分析的工程结构不确定性问题研究归结为以下4个方面: 不确定性结构系统 的区间有限元分析; 基于区间的非概率可靠性分析; 工程结构区间反演分析; 基于区间参数 的结构优化设计. 分析评价了国内外在这几个方面的研究成果及其最新进展, 同时指出目前 研究中存在的问题和研究的方向.

CURRENT RESEARCH AND PROSPECTS ON INTERVAL ANALYSIS IN ENGINEERING STRUCTURE UNCERTAINTY ANALYSIS

Stochastic analysis method and fuzzy analysis method are widely used in uncertainty analysis of engineering structures. Recently, interval analysis method is gradually known and becomes a new uncertainty analysis method. Interval analysis method is mainly used for engineering structures with interval properties. Interval analysis method shows its merits when the statistical information does not available for the parameters' probability distributions or related functions except the intervals of the parameters. In this paper, interval analysis method and its applications in engineering structure uncertainty analysis are overviewed. The applications are summarized into four parts, that is, interval finite element analysis in uncertainty of engineering structures; the probability based on interval analysis; interval inverse analysis method of engineering structures; structural optimum design based on interval parameters. The research results and recent advances in these parts are analyzed, and the existing problems and future trends in these fields are discussed.