Probabilistic relative entropy in elasto‐plasticity using the iterative generalized stochastic stress‐based Finite Element Method

Author:

Kamiński Marcin1ORCID,Bredow Rafał1ORCID

Affiliation:

1. Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering Lodz University of Technology Łódź Poland

Abstract

AbstractThe generalized iterative stochastic perturbation approach to the stress‐based Finite Element Method has been proposed in this work. This approach is completed using the complementary energy principle, Taylor expansion of the general order applicable to all random functions and parameters as well as nodal polynomial response bases determined with the use of the Least Squares Method. The main aim of this elaboration is the usage of such a probabilistic approach to determine Bhattacharyya relative entropy for some nonlinear engineering stress analysis with uncertainty. Mathematical apparatus with its numerical implementation has been used to study elastoplastic torsion of some prismatic bar with Gaussian material uncertainty and the corresponding reliability measures. This problem has been solved using the Constant Stress Triangular (CST) plane finite elements, the modified Newton–Raphson algorithm, whereas the first four probabilistic characteristics resulting from the iterative generalized stochastic perturbation method have been contrasted with these obtained with the crude Monte‐Carlo sampling and the semi‐analytical probabilistic approach.

Funder

Narodowe Centrum Nauki

Publisher

Wiley

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