  The LATIN method has been developed and successfully applied to a variety of
deterministic problems, but few work has been developed for nonlinear
stochastic problems. This paper presents a stochastic LATIN method to solve
stochastic and/or parameterized elastoplastic problems. To this end, the
stochastic solution is decoupled into spatial, temporal and stochastic spaces,
and approximated by the sum of a set of products of triplets of spatial
functions, temporal functions and random variables. Each triplet is then
calculated in a greedy way using a stochastic LATIN iteration. The high
efficiency of the proposed method relies on two aspects: The nonlinearity is
efficiently handled by inheriting advantages of the classical LATIN method, and
the randomness and/or parameters are effectively treated by a sample-based
approximation of stochastic spaces. Further, the proposed method is not
sensitive to the stochastic and/or parametric dimensions of inputs due to the
sample description of stochastic spaces. It can thus be applied to
high-dimensional stochastic and parameterized problems. Four numerical examples
demonstrate the promising performance of the proposed stochastic LATIN method.
