MAXIMUM ENTROPY UNCERTAINTY MODELING AT THE FINITE ELEMENT LEVEL FOR HEATED STRUCTURES

The focus of this paper is on the introduction of uncertainty on structural properties, including the thermal expansion coefficient, on linear finite element models of heated structures. A “mesoscale” approach is adopted here in which the uncertainty is introduced directly on the elemental matrices and vectors of each element by randomizing those corresponding to the mean model following the maximum entropy approach and recent work by the authors. As such, the approach is applicable to finite element models developed in commercial software in which the elemental matrices can be exported. In this approach, the elemental stiffness matrix and the thermal force vectors are regrouped into an extended, positive definite matrix which is randomized. However, the uncertainty can be introduced either separately or jointly on the stiffness matrix and the thermal force vectors. The parameters of this uncertainty modeling include the overall levels of uncertainty on the stiffness matrix and the thermal force vectors and the correlation lengths of these properties. It is noted that the proposed approach is also applicable to structures with piezoelectric components when the piezoelectric effect is modeled using the thermal analogy.