Speaker
Description
This work's main aim is to quantify uncertainty in some elastoplasticity problems using probabilistic entropy and probabilistic distance. Classical theoretical and computational approaches based on probabilistic moments and characteristics are contrasted with Shannon entropy in order to obtain and test a single uncertainty measure in certain nonlinear problems of solid mechanics. A general hypothesis that probabilistic entropy may serve for this purpose is tested using the Stochastic Finite Element Method (SFEM) approach implemented using Monte-Carlo simulation. Probabilistic moments computed as the referential solution are determined using a triple numerical strategy, where Monte-Carlo simulation is accompanied by the perturbation technique as well as the semi-analytical approach. This SFEM implementation has been completed using the ABAQUS system and a computer algebra system MAPLE. Additionally, the probabilistic distance (relative probabilistic entropy) apparatus is presented and applied to study two certain limit functions defined using admissible and extreme deformations and stresses in the elastoplastic regime. It has been demonstrated that such a relative entropy may serve for reliability assessment and exhibit very similar variations in addition to the input uncertainty level as the classical First Order Reliability Method index. A few mathematical models of probabilistic distance will be discussed including Bhattacharyya, Hellinger, Kullback-Leibler, and also Jensens models. Some issues concerning the existence of the integrals representing probabilistic distance will be discussed separately. A few computational experiments illustrating this approach will discuss uncertainty quantification in the Ramgberg-Osgood constitutive law, probabilistic convergence of the Monte-Carlo simulation, numerical error of probabilistic entropy determination as well as an influence of a choice of the probability density function.
