基于随机有限元的结构.doc

摘 要
结构可靠度的概念来源于工程实践，在各类工程结构中，存在着很多随机因素的影响，如结构的物理特性、几何参数等结构本身的特性及结构所承受的荷载。因此，对结构三维空间结构进行随机分析并评价其可靠性就显得非常有必要。基于蒙特卡洛直接抽样法，通过大量的抽样，对结构系统进行可靠性分析，其计算精度相对较高，但对于大型复杂结构系统，采用此方法费时较多，实用性很差。因此，本文采用随机有限元法对结构可靠性进行分析。
本文首先介绍了可靠性设计的国内外研究现状及发展趋势，接着介绍了随机有限元理论及确定性有限元分析的方法，然后阐述了神经网络及遗传算法，并对其进行简单运用。在结构可靠性分析中，对梁板结构和船舱段结构简例进行分析，首先建立梁板结构单元的安全余量，利用改进的一次二阶矩法计算各失效模式的安全余量，采用分枝限界法找出主要失效模式，利用概率网络估算技术法计算结构系统的失效概率并进行敏度分析。然后将梁板结构的可靠性分析与基于蒙特卡洛直接抽样法的计算结果进行比较，得出本文方法的可行性。在结构优化中，通过神经网络和遗传算法，对船舱段结构进行优化设计，每代遗传操作中只需以上可靠性方法计算一次结构系统可靠性指标，将该代最优解对应的数据加入神经网络的训练样本，从训练样本中删除最劣样本，使样本不断处于更新状态。通过两种算法的结合，利用随机有限元法的基本理论，建立了一套完整的基于可靠性的随机结构系统优化设计方法。
最后，本文开发了基于随机有限元的结构可靠性分析及优化原型系统，考虑材料的强度、梁板元的尺寸和外载荷等均为随机变量的三维梁板空间结构，通过几个实例说明了本文方法的可行性，并研究了优化算法对优化结果的影响，得出了一些有益的结论。
关键词 随机有限元法；分枝限界法；改进的一次二阶矩法；安全余量；可靠性优化


Abstract
The concept of structure reliability comes from the engineering practice. In all kinds of engineering structure, there are many random factors, such as structural physical characteristics, geometric parameters which are structure characteristics of itself and the load. Therefore, it is very necessary to make reliability analysis and eva luation of the 3d spatial stochastic structure. Based on direct Monte-Carlo sampling method, the computing accuracy is relative taller for structural system reliability analysis through a lot of sampling. But for large complex structure system, using this method spends more time and the practicability is very poor. So this paper adopts stochastic finite element method to the structural reliability analysis.
This paper firstly introduces the domestic and foreign research situation and development trend of the reliability design. Then introduce the stochastic finite element theory and deterministic finite element analysis method. Expound the neural network and genetic algorithm, and carry on the simple example. In the structural reliability analysis, analyse the example of the beam and shell structure and the cabin paragraph structure. Firstly establish the unit safety margins of beam and shell structure. Calculate the various failure modes of the safety margins with using adapted first-order second-moment method. Use branch and bound method to identify major failure modes. Finally, use the failure mode correlation and PNET method to calculate the failure probability of structural systems and the sensitivity analysis. Compare the calculation results of structure reliability analysis with the results of the direct Monte-Carlo sampling method, conclude the feasibility method of this paper. In the structural optimization, use the neural network and genetic algorithm to have the optimization design of the structure of the cabin paragraph. Calculate the structural system reliability index one time with the above traditional method in each generation of genetic operations. Join the corresponding data of the generation optimal solution of in the training samples and delete the inferior samples from the training sample to update the training samples of neural network. Through the combination of two algorithms, using the basic theory of the stochastic finite element method, has established a complete method of the optimization design based on the reliability of the stochastic structural system.
Finally, this paper develops the prototype system of the reliability analysis and optimization of the structure based on stochastic finite element. Consider the random variable of the material strength, the dimensions of beam and shell units and outer loads of the 3d beam and shell spatial structure. Through several examples illustrate the feasibility of the method, and study the influence of the optimization algorithm, obtain some useful conclusions.
Keywords stochastic finite element method; branch and bound method; adapted first- order second-moment method; safety margin; reliability Optimization


目 录
摘 要 I
Abstract II
第1章 绪论 1
1.1 选题背景、意义及实用价值 1
1.2 结构可靠性设计国内外研究现状 1
1.3基于随机有限元结构优化研究现状及发展趋势 2
1.3.1随机有限元国内外研究现状 2
1.3.2基于可靠性优化研究现状及发展趋势 3
1.4 论文研究内容及章节安排 5
1.4.1 论文研究内容 5
1.4.2 章节安排 5
1.5 本章小结 6
第2章 随机有限元理论分析研究 ..