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.

翻译：LATIN方法已发展并被成功应用于各类确定性问题的求解，但针对非线性随机问题的研究尚不充分。本文提出一种随机LATIN方法，用于求解随机和/或参数化的弹塑性问题。为此，将随机解分解为空间、时间与随机三个维度，并通过一组空间函数、时间函数与随机变量三元组乘积之和进行逼近。每个三元组采用贪心策略，通过随机LATIN迭代逐一计算。该方法的高效性体现在两个方面：继承经典LATIN方法的优势有效处理非线性特性；基于样本的随机空间近似方法高效处理随机性和/或参数。此外，由于采用样本描述随机空间，该方法对输入随机和/或参数的维度不敏感，因此可适用于高维随机与参数化问题。四个数值算例展示了所提出的随机LATIN方法的优越性能。