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 theYoung's modulus being considered as a random field. For a small variation, the stochasticgoverning differential equation and the boundary conditions of the problem are first decomposedinto two sets of equations and conditions corresponding to a mean valueproblem and a deviationproblem, respectively. According to the similarity between the above two sets of equations andconditions, analytical solutions corresponding to different covariance structures and fluctuationscales are then obtained. On this basis, the sensitivity study of the covariance functions on thestructural response is carried out. It is shown that different covariance structures have certain effects onthe stochastic results, but have little influence on the solutions when the fluctuation scales areeither small or large. The exact solutions obtained in this paper mayalso be used to verify the validity of other numerical methods.