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Nb3Sn magnets with a nominal operation field of ~15 T are being considered for the Large Hadron Collider (LHC) energy upgrade High-Energy Large Hadron Collider (HE-LHC) and a post-LHC future circular collider. To demonstrate the feasibility of 15-T accelerator quality dipole magnets, the U.S. magnet development program is developing a single-aperture 15-T Nb3Sn dipole demonstrator based on a 4-layer graded cos-theta coil with 60 mm aperture and cold iron yoke. The main design challenges for 15-T accelerator magnets include large Lorentz forces at this field level. To counteract them, an innovative mechanical structure based on a vertically split iron yoke, locked by large aluminum IC-clamps and supported by a thick stainless steel skin, has been developed at Fermilab. To study the performance of the structure, a parametric multiphysics finite element analysis (FEA) model has been set up. This paper describes the numerical model as well as the results of a sensitivity analysis of the effect of geometrical tolerances and assembly parameters. [ABSTRACT FROM AUTHOR]