Stochastic finite element method for elasto-plastic body

This paper proposes a Stochastic Finite Element Method (SFEM) for non-linear elasto-plastic bodies, as a generalization of the SFEM for linear elastic bodies developed by Ghanem and Spanos who applied the Karhunen–Loeve expansion and the polynomial chaos expansion for stochastic material properties and field variables, respectively. The key feature of the proposed SFEM is the introduction of two fictitious bodies whose behaviours provide upper and lower bounds for the mean of field variables. The two bounding bodies are rigorously obtained from a given distribution of material properties. The deformation of an ideal elasto-plastic body of the Huber–von Mises type is computed as an illustrative example. The results are compared with Monte-Carlo simulation. It is shown that the proposed SFEM can satisfactorily estimate means, variances and other probabilistic characteristics of field variables even when the body has a larger variance of the material properties. Copyright © 1999 John Wiley & Sons, Ltd.