This work deals with outputs of interest for linear elastic F.E. analysis in the presence of uncertainties (material, loads...). The objective of this paper is precisely to develop tools for the assessment of linear stochastic models. Our approach relies on an extension of the constitutive relation error method, which is a very effective verification tool in the deterministic case. In order to obtain bounds of outputs of interest, one must solve an adjoint problem. In order to do that, one must build for the direct and adjoint problems an associated admissible displacement-stress pair. Then, bounds corresponding to a given level of certainty can be calculated. Theses bounds take into account the errors due to the finite element discretization as well as the errors due to the stochastic approximation method.
The method is illustrated through numerical tests. These tests demonstrate the capabilities of this new tool in providing bounds which can be of direct use to the designer. With such bounds, calculation can lead to certification, even in the case of uncertain loading cases.