悬臂轴拉杆一阶随机分析的解析解

针对悬臂轴拉杆在自由端受集中力问题进行了随机分析，其中考虑了轴拉杆杨氏模量的变异，在小变异情况下获得了不同相关结构与相关长度下问题的解析解，并就结果对相关结构的敏感性进行了讨论．

EXACT SOLUTIONS FOR FIRST-ORDER STOCHASTIC ANALYSIS OF AXIALLY-LOADED CANTILEVER BARS

This paper presents a stochastic analysis of an axially-loaded cantilever bar with the Young's modu- lus being considered as a random field. For a small varia- tion, the stochastic governing differential equation and the boundary conditions of the problem are first decomposed into two sets of equations and conditions corresponding to a mean value problem and a deviation problem, re- spectively. According to the similarity between the above two sets of equations and conditions, analytical solutions corresponding to different covariance structures and fluc- tuation scales are then obtained. On this basis, the sensi- tivity study of the covariance functions on the structural response is carried out. It is shown that different covari- ance structures have certain effects on the stochastic re- sults, but have little influence on the solutions when the fluctuation scales are either small or large. The exact so- lutions obtained in this paper may also be used to verify the validity of other numerical methods.