【作者】 雒卫廷；

【导师】 陈建军；

【作者基本信息】 西安电子科技大学 ， 机械制造及其自动化， 2003， 硕士

【摘要】 本文基于加权残值法和矩法的特点，提出了随机结构分析的一种新方法，并从理论上给出了其统一的表述。该方法的基本思想是利用加权残值法获得问题解的近似函数表达式，在此基础上利用求解随机变量函数的矩法求得随机函数的一、二阶矩等统计数字特征。它具有加权残值法和矩法两者固有的全部优点，其原理简单、计算简便、且能够获得随机结构系统中每一参数的随机性对结构反应的影响。文中将这一方法成功地应用于随机结构的静力学分析、稳定性问题、动力特征值求解和动力响应分析之中，对随机梁、板结构编制了静力分析计算通用程序，证明了此法的正确性、有效性。此外，基于这一方法，提出了一种对边界条件随机性处理的方法，并在静力学问题分析中予以实现。通过对若干算例的结果分析，获得了许多对随机结构设计有价值的结论。更多还原

【Abstract】 Based on Method of Moment and Method of Weighted Residuals, a new analysis method for the stochastic structures is proposed and described as a unified form in this paper. The main idea of this method include two steps: at first, the approximate expression of function is obtained by Method of Weighted Residuals; then the first and second moment of the random function can be calculated with Method of Moment. It has all of the advantages of Method of Moment and Method of Weighted Residuals such as simple principle, handy calculation, and the effect to structural reaction from randomness of each structural parameter can be gained. The feasibility and validity of the method have been proved by the examples of statical analysis, stability problem, dynamical eigenvalue calculation, and dynamical response analysis. The general procedure of statical analysis for beam and plate is programed. Based on the method, a new way to deal with the randomicity of boundary condition is advanced and implemented in statical analysis. By analyzing the results of the examples, many useful conclusions for design of stochastic structure are obtained.更多还原