Uncertainty Evaluation in Euler-Bernoulli and Timoshenko Bending Statics Problems

EasyChair Preprint no. 543

Abstract

The error estimate of an adopted model is one of the main challenges in the quantification of uncertainty and in predictive science. For computational models of complex physical systems, the model error - also known as ‘random process’ or ‘model inadequacy’ - is frequently the major contributor to general predictive uncertainty. In stochastic mechanics, process uncertainties are associated to the material and geometry of the structural elements as well as to the load on the structure and, from the random process, one seeks to quantify the variability of the responses, generally associated to stresses and strains. Uncertainty is dealt with as a multivariate stochastic field where the system properties are modeled through their probability distribution. The Monte Carlo simulation emerges as a traditional model of reliability evaluation in order to solve the stochastic variational problem formulated using finite elements, but, for more complex systems, the computing costs of this model becomes prohibitive. The proposal of the present work is to study, apply, and evaluate the Monte Carlo λ-Neumann simulation model with a numerical methodology and strategy to quantify uncertainty when applied to the traditional Euler-Bernoulli beam bending theory and the Timoshenko bending and rotation theory. MCS N-λ is based on the Neumann series and, for problems to which it was applied, it presented a satisfactory performance regarding a reduction in processing time and also in the non-intrusiveness of the computer program.

Keyphrases: Beam theory, Monte Carlo simulation, Stochastic mechanics

@Booklet{EasyChair:543,
  author = {Roberto Mauro Félix Squarcio and Claudio Roberto Ávila Silva Junior},
  title = {Uncertainty Evaluation in Euler-Bernoulli and Timoshenko Bending Statics Problems},
  howpublished = {EasyChair Preprint no. 543},
  doi = {10.29007/n1r5},
  year = {EasyChair, 2018}}