A stochastic LATIN method for stochastic and parameterized elastoplastic analysis

TL;DR

This paper introduces a stochastic LATIN method that efficiently solves high-dimensional stochastic and parameterized elastoplastic problems by decoupling the solution into spatial, temporal, and stochastic components and using a greedy iterative approach.

Contribution

It extends the classical LATIN method to stochastic problems, enabling efficient handling of high-dimensional stochastic and parametric inputs with a sample-based approximation.

Findings

Demonstrated high efficiency through numerical examples.

Effective handling of high-dimensional stochastic spaces.

Robust performance in elastoplastic analysis.

Abstract

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.