  Practical structural engineering problems often exhibit a significant degree
of uncertainty in the material properties being used, the dimensions of the
modeled structures, etc. In this paper, we consider a cantilever beam and a
beam clamped at both ends, both subjected to a static and a dynamic load. The
material uncertainty resides in the Young's modulus, which is modeled by means
of one random variable, sampled from a univariate Gamma distribution, or with
multiple random variables, sampled from a Gamma random field. Three different
responses are considered: the static elastic, the dynamic elastic and the
static elastoplastic response. In the first two cases, we simulate the spatial
displacement of a concrete beam and its frequency response in the elastic
domain. The third case simulates the spatial displacement of a steel beam in
the elastoplastic domain. In order to compute the statistical quantities of the
static deflection and frequency response function, Multilevel Monte Carlo
(MLMC) is combined with a Finite Element solver. In this paper, the
computational costs and run times of the MLMC method are compared with those of
the classical Monte Carlo method, demonstrating a significant speedup of up to
several orders of magnitude for the studied cases.
