Maximum entropy structural-thermal uncertainty modeling at the finite element level

A recently proposed approach for the modeling of uncertainties in finite element models of linear structural or thermal problems is extended here for heated structures behaving linearly. The uncertainty is introduced at the level of each finite element by randomizing an elemental, positive semi definite matrix that includes both the stiffness matrix and the thermal loading using the maximum entropy concept. The approach is characterized by two groups of parameters, one expressing the overall level of uncertainty of the structural and thermal loading terms while the other group are the correlation lengths 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.