Lessons pertaining to the finite element method for stochastic problems, learned from simplest example

The simplest structure – uniform bar with stochastic modulus of elasticity, but other properties and the excitation being deterministic is studied in the view to extract some useful lessons for the finite element method in stochastic setting. Closed-form solutions as well as various approximations are derived for the probabilistic characteristics of the tip displacement. Improved perturbation method is confronted on one hand, with classical perturbation method, and, on the other, with polynomial chaos expansion in conjunction with the Galerkinʹs method.