A possibilistic finite element method for sparse data

Abstract

This paper presents a ‘possibilistic’ application of the finite element method (FEM) considering a linear elastic body with sparse information of input design variables. The corresponding uncertainty characteristic is referred to as ‘imprecise probability’. Each input variable is constituted as a possibility distribution comprising a family of probability distributions to account for sparse experimental data. As a special case, we consider isotropic material behaviour with imprecise input variables. Computational approaches involving a ‘probability-possibility’ transformation are applied in order to transform sparse experimental information into corresponding possibility distributions. Finally, in a representative example for a plate with a ring hole the possibility for a quantity of interest is calculated using the alpha-level discretisation technique under consideration of the interaction between shear and bulk modulus.