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

By M. Anders, Muneo Hori. 2001

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Strategy for selecting representative points via tangent spheres in the probability density evolution method (2008, unknown): “In addition, the extensions based on an incremental scheme were also tried in non-linear static problems, but the accuracy was greatly poorer than the linear counterpart [15, 16].”
The stochastic finite element method: Past, present and future (2009, methodology): “The first application of the method to elasto-plastic problems can be found in [3] where plastic and failure analysis of earth faults is attempted by introducing some simplifying assumptions.”
Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos (2002, methodology): “A similar iteration technique was used in [34] for stochastic modeling of elasto-plastic body problems with the Hermite-chaos and fast convergence was reported too.”
Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields (2007, methodology): “[1,2,5,7,8,15,33,45].”
Scale effects in plasticity of random media: status and challenges (2005, methodology): “A different approach was recently advanced by Anders and Hori (1999, 2001) , who employed a stochastic finite element approach based on the Karhunen–Loe `ve polynomial chaos expansion (Ghanem and Spanos, 1991) to study 3-D softening elasto-plastic bodies.”