A stochastic LATIN method for stochastic and parameterized elastoplastic analysis

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. Five numerical examples demonstrate the promising performance of the proposed stochastic LATIN method.

Automated summary

This paper presents a stochastic LATIN method to solve stochastic and/or parameterized elastoplastic problems. The method approximates the stochastic solution by decomposing it into spatial, temporal, and stochastic spaces and using a set of triplets of spatial functions, temporal functions, and random variables. The method efficiently handles nonlinearity and randomness and/or parameters.