【作者】 苏静波；

【导师】 邵国建； 刘宁；

【作者基本信息】 河海大学 ， 工程力学， 2006， 博士

【摘要】 通常的结构分析模型是建立在确定性物理意义上的，即把分析过程中各种因素作为确定性物理量来进行处理。但是，实际工程结构分析中存在各种各样的不确定性，如果硬将这些不确定性因素作为确定性信息来处理，有时会得出矛盾的或很不合理的结果。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。本文针对当前区间分析方法中的热点和难点进行了研究，并将其应用于工程结构计算中。主要工作内容如下： 1)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的研究归纳为以下四个方面：不确定性的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和基于区间参数的结构优化设计。 2)针对区间运算导致区间扩张问题，分析了截断处理方法、运算顺序处理方法，提出了子区间摄动处理方法，并给出了子区间摄动方法可以收敛到真解区间的说明。分析了区间有限元摄动解法、单调性组合解法等，提出了Monte-Carlo区间有限元方法和基于单元的子区间参数摄动有限元方法，并给出了可以获得较为精确解区间的子区间划分数目的计算公式；将区间有限元分析方法从一维的杆件结构分析拓广到二维实体结构分析中。 3)遗传算法对全局搜索能力较强、局部搜索能力较弱，而模拟退火算法局部搜索能力较强、全局搜索能力较弱；文中将遗传算法与模拟退火算法相结合给出了一种遗传模拟退火算法，并编制了相应的程序；将该优化方法应用于区间有限元优化分析和区间反分析计算中。 4)基于Marc软件分析非线性程度高、计算速度快的优点，对其进行了二次开发，实现了网格及其计算数据的自动多次生成，以及岩土体非线性弹性和弹塑性本构模型、各种复杂边界条件的施加等；提出了基于Marc软件的区间参数优化的区间有限元分析方法，针对重力坝、地下隧洞结构进行了区间有限元优化分析。 5)为了解某一参数的变化对结构响应的影响程度，提出了参数敏感性的区间分析方法，可以获得模型参数对决策目标的敏感性因子矩阵；通过对一平面应变结构地基模型的分析，得出了土体Duncan-Chang E_t-ν_t模型的八个参数的敏感性因子矩阵。考虑量测信息的不确定性，针对线弹性结构，提出了参数摄动法区间有限元逆反分析模型、基于区间算法的区间有限元反分析模型以及基于单元的参数摄动法区间有限元逆反分更多还原

【Abstract】 Accustomed structural analysis models are based on certain physical ideas. That is to say: all kinds of physical factors are considered as certain datum in the process of analysis. But plenty of uncertain factors exist in factual engineering structural analysis. If the uncertain factors are considered as certain information, the inconsistent or unreasonable results will be received. 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 is not available for the parameters’ probability distributions or related functions but the intervals of the parameters can be known. In this paper, the hotspots and difficulties of interval analysis method are discussed and the results are applied to engineering practices. The contents are as follows:1) Interval analysis method and its applications in engineering structure uncertainty analysis are overviewed in this paper. 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 subjects are analyzed appraised. And the existing problems and future trends in these fields are discussed.2) The interval-truncation approach and interval operation orders approach are given for interval expansion. Further, the sub-interval perturbation approach is putted forward and the convergence property of the method is explained. Interval perturbation finite element method and monotony-combination interval finite element method and otherwise methods are analyzed. The Monte-Carlo interval finite element method and sub-interval parameter perturbation finite element method based on elements are putted forward and the approximate formulae of the sub-interval numbers for relatively accurate interval are given. The interval finite element analysis method is extended from one-dimension truss member and beam structure to two-dimension plane structure.3) Genetic algorithm has powerful capability of global search and lower capability of local search, however, simulated annealing algorithm has powerful capability of local search and lower capability of global search. One genetic and simulated annealing algorithm is given更多还原