Stochastic Finite Element Analysis of Simple Beams

Abstract

A method of stochastic finite element analysis is developed for solving a variety of engineering mechanics problems in which physical properties exhibit one‐dimensional spatial random variation. The method is illustrated by evaluating the second‐order statistics of the deflection of a beam whose rigidity varies randomly along its axis. A key component of the approach is a new treatment of the correlation structure of the random material property in terms of the variance function and its principal parameter, the scale of fluctuation. The methodology permits efficient evaluation of the matrix of covariances between local spatial averages associated with pairs of finite elements. Numerical results are presented for a cantilever beam, with deformation controlled by shear, subjected to a concentrated force at its free end or to a uniformly distributed load.