【作者】 于莉；

【导师】 徐慧；

【作者基本信息】 天津大学 ， 船舶与海洋结构物设计制造， 2004， 硕士

【摘要】 将工程问题抽象为研究所用的理论模型时,总会遇到一些不确定因素。可以说不确定性的问题广泛存在于工程结构分析和设计过程之中,不能简单地予以忽略。目前有三种解决不确定性问题的方法,如:概率方法、模糊方法和区间方法。而区间分析方法对于无法得到具体的概率统计数据的不确定因素的分析不失为一种有效的方法。本论文对这种方法进行了详细的研究讨论,并针对目前还少有人研究的具有材料非线性的不确定结构系统的区间分析方法进行了深入的研究讨论并针对计算结果易于扩张这一区间计算的主要缺陷,采用把区间函数的计算和区间方程组的求解转化为利用相应的全局优化问题来近似求解结构静态响应解的区间边界值的问题。在求解全局优化问题的数值计算上采用了实数编码遗传算法。编制了相应的计算软件。文中针对典型的非线性梁及桁架结构系统从三个不同的角度进行了充分的讨论研究。三种情况为:(1)结构参数是确定的,使结构部件材料出现非线性的外载荷的临界值以及结构系统在临界外载荷作用下的静态响应。(2)结构参数具有不确定的区间特性时,使结构部件材料出现非线性的外载荷的临界值范围。(3)结构参数和外载荷均具有不确定的区间特性,结构系统的静态响应范围。更多还原

【Abstract】 When engineering problems are abstracted to theoretical models, someuncertain factors maybe appear. Uncertainties widely exist in the process ofstructural analysis and design for engineering, which can not be ignored simply. Atpresent, there are three main methods for uncertain modeling, such as probabilitymethod, fuzzy method and interval method. Moreover interval analysis method is aneffective method for the analysis of uncertain factors which real probability statisticdatum is not obtained.This method is discussed in detail in this paper. The intervalanalysis method for uncertain structure system with nonlinear material on whichthere is no much research yet is studied and discussed deeply. Becauseoverestimation is one main limitation in interval computation, computation ofinterval function and solution of interval equations set are transformed into generaloptimization problems to determine the boundary of each interval element in thesolution in this work. Genetic arithmetic of real number coding is used to solvegeneral optimization problems. Corresponding calculation software is edited.Three different situations for typical nonlinear beam and truss system are studiedand discussed sufficiently. The three situations are: (1) structural parameters arecertain, the critical value of load which cause structural parts appear nonlinear ofmaterial and the static response of structure system under the corresponding criticalload are discussed. (2)structural parameters are uncertain, the bound of critical valueof load which cause structural parts appear nonlinear of material isdiscussed.(3)structural parameters and load are uncertain, the bound of static responseof structure system is discussed.更多还原