An introduction to nonlinear problems with random parameters by the Stochastic perturbation-based FEM

The main aim of this paper is to present an algorithm and the solution to the nonlinear problems with random parameters. The methodology is based on the generalized nth order stochastic perturbation method and, on the other hand, on the Finite Element Method adjacent to the physical and geometrical nonlinearities. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is proposed in two different ways – thanks to the straightforward differentiation of the initial incremental equation and, separately, using the modified Response Function Method. This approach is illustrated with the analysis of the simply supported elastoplastic beam loaded centrally with the concentrated force, where the probabilistic moments for the limit load and the reliability indices are determined via the stochastic symbolic computations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)