Three-dimensional stochastic finite element method for elasto-plastic bodies

A new stochastic finite element method (SFEM) is formulated for three-dimen sional softening elastoplastic bodies with random material properties. The method is based on the Karhunen-Loeve and polynomial chaos expansions, and able to efficiently estimate complete probabilistic characteristics of the response, such as moments or PDFs. To reduce the computational complexity i n the three-dimensional setting, two alterations are made with respect to t he two-dimensional SFEM proposed earlier by the authors. First, a variabili ty preserving modification of the Karhunen-Loeve expansion is rigorously de rived and applied in the stochastic discretization of random fields represe nting material properties. Second, an efficient algorithm for parallel proc essing is developed, with time consumption being the same order as for an o rdinary FEM, rendering the proposed SFEM an effective alternative to Monte Carlo simulation. The applicability of the proposed method to stochastic an alysis of strain localization is examined using Monte-Carlo simulation. The n, it is applied to a fault formation problem which is a recent concern of earthquake engineering. Ground surface layers are modelled by a softening e lastoplastic body, and the evolution of probabilistic characteristics of th e rupture process is analysed in detail. Some practical observations are ma de regarding the nature of the fault formation from the stochastic viewpoin t. Copyright (C) 2001 John Wiley & Sons, Ltd.