Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems

A novel approach is proposed for the modeling of uncertainties in finite element models of linear structural or thermal problems. This uncertainty is introduced at the level of each finite element by randomizing the corresponding elemental matrices (e.g., mass, stiffness, conductance) using the maximum entropy concept. The approach is characterized by only two parameters, one expressing the overall level of uncertainty while the other is the correlation length underlying the random elemental matrices. As it proceeds from the finite element mean model matrices, the modeling can be performed from finite element models constructed in commercial software. In fact, the approach is exemplified on a structural example developed within Nastran with the assembly of the random elemental matrices performed outside of this software.